Mining  ••' 


LIBRARY 


UNIVERSITY  OF  CALIFORNIA. 


Clas. 


MAGNETIC  INDUCTION  IN  IRON 
AND  OTHER  METALS. 


BY 


J.     A.     EW1NG, 

li 

M.A.,   F.R.S.,    M.INST.C.E., 


PROFESSOR   OF   MECHANISM    AND   APPLIED   MECHANICS   IN   THE    UNIVERSITY    OF 

CAMBRIDGE, 

FELLOW   OF   KING'S    COLLEGE,    CAMBRIDGE. 


THIRD     EDITION,     REVISED. 


UNIVERSITY 

OF  / 

i F OR tjifc^  . 

THE     D.     VAN     NOSTRAND     COMPANY, 
23,  MURRAY  STREET,  AND  27  WARREN  STREET. 

LONDON : 
THE  ELECTRICIAN  "  PRINTING  AND  PUBLISHING  COMPANY, 

LIMITED, 

SALISBURY  COURT,  FLEET  STREET,  E.G. 

JAPAN  :  Z.  P.  Maruya  &  Co. ,  14,  Nihonbashi  Tori  Sanchome,  Tokyo. 
INDIA  :  Thacker,  Spink  &  Co.,  Calcutta. 

Higginbotbam  &  Co.,  Madras. 

AUSTRALIA:  George  Robertson  &  Co.,  Melbourne,  Sydney,  Adelaide 
and  Brisbane. 

All  Rights  lleserved. 


£? 


Printed  and  Published  by 

THE  ELECTRICIAN"  PRINTING  AND  PUBLISHING  co.,  LTD. 

1,  2  and  3,  Salisbury  Court,  Fleet  Street, 

London,  E.C. 


PREFACE. 


DURING  recent  years,  and  especially  during  the 
last  ten,  our  knowledge  of  the  physical  facts  of 
Magnetisation  has  made  a  marked  advance.  Perhaps 
no  subject  has  profited  more  by  the  beneficent  reaction 
of  Practice  on  Science.  The  labours  of  a  number  of 
observers  have  made  it  possible  to  present  a  connected 
account  of  the  phenomena  of  magnetic  induction  and  of 
the  distinctive  qualities  of  the  magnetic  family  of  metals. 
There  are  still,  of  course,  many  questions  for  experiment 
to  answer  ;  but  a  text-book  of  the  subject  may  now  be 
written  with  some  degree  of  continuity  and  completeness. 

In  attempting  this  task,  the  author  has  not  ap- 
proached the  matter  from  the  standpoint  of  the  scientific 
historian.  He  has  been  more  concerned  to  tell  of  things 
discovered  than  of  discoverers.  In  many  instances, 
therefore,  the  work  of  early  observers  is  passed  over 
with  no  mention,  or  with  the  briefest,  because  later 
experiments  are  found  to  deal  with  the  same  points  in 
a  more  conclusive  or  more  exhaustive  way. 

The  author's  aim  has  been  to  present  the  subject  in 
sufficient  detail  to  satisfy  scientific  students,  as  well  as  to 
meet  the  wants  of  those  who  may  turn  to  the  book  in 
quest  of  data  for  application  to  matters  of  practice. 
Particulars,  which  will  facilitate  reference  to  the  original 

4 

179327 


IV.  PREFACE. 

memoirs  in  which  researches  are  described,  have  in  all 
cases  been  given  for  the  assistance  of  those  who  may 
wish  to  pursue  the  subject  further  than  a  short  text- 
book can  well  take  them. 

After  an  introductory  chapter,  which  attempts  to 
explain  the  fundamental  ideas  and  the  terminology,  an 
account  is  given  of  the  methods  which  are  usually  em- 
ployed to  measure  the  magnetic  qualities  of  metals. 
Examples  are  then  quoted,  showing  the  results  of  such 
measurements  for  various  specimens  of  iron,  steel,  nickel, 
and  cobalt.  A  chapter  on  Magnetic  Hysteresis  follows, 
and  then  the  distinctive  features  of  induction  by  very 
weak  and  by  very  strong  magnetic  forces  are  separately 
described,  with  further  description  of  experimental 
methods,  and  with  additional  numerical  results.  The 
influence  of  Temperature  and  the  influence  of  Stress  are 
/lext  discussed.  The  conception  of  the  Magnetic  Circuit 
is  then  explained,  and  some  account  is  given  of  experi- 
ments which  are  best  elucidated  by  making  use  of  this 
essentially  modern  method  of  treatment.  The  book 
concludes  with  a  chapter  on  the  Molecular  Theory  of 
Magnetic  Induction  ;  and  the  opportunity  is  taken  to 
refer  to  a  number  of  miscellaneous  experimental  facts, 
on  which  the  molecular  theory  has  an  evident  bearing. 

Throughout  the  book  the  author  has  endeavoured 
to  familiarise  the  student'  with  the  notion  of  intensity  of 
magnetisation  (|)  as  well  as  with  the  notion  of  magnetic 
induction  (B)-  It  has  been  urged  by  some  writers  that 
the  alternative  which  is  in  this  way  offered  is  unnecessary 
and  confusing,  and  that  if  we  keep  "B"  we  may  dispense 
with  "  |."  The  scientific  value  and  the  practical  utility 
of "  B "  are  so  obvious  that  no  one  proposes  to  avoid 
using  that.  It  is  "  |  "  that  we  are  told  must  go.  In  this 


PREFACE.  V. 

cry  the  author  is  by  no  means  disposed  to  join.  It  is 
not  too  much  to  say  that  in  stating  the  magnetic  qualities 
of  a  metal  the  quantity  "|"  is  of  primary  importance. 
The  facts  of  saturation,  the  molecular  theory,  and  the 
phenomena  of  magneto-optics,  all  demonstrate  its  phy- 
sical reality  and  its  fundamental  interest. 

The  author  would  take  this  opportunity  to  repeat  an 
acknowledgment,  already  made  elsewhere,  of  the  assist- 
ance most  willingly  and  ably  rendered  by  a  number  of 
his  pupils  in  carrying  out  experiments  on  some  of  the 
subjects  with  which  this  book  deals.  Messrs.  Tanaka- 
date,  Fujisawa,  Tanaka,  and  Sakai,  in  Japan,  and 
Messrs.  W.  Low,  Cowan,  D.  Low,  and  Frew,  in 
Dundee,  have  been  skilful  and  sympathetic  collaborators, 
whose  interest  was  as  lively  as  their  patience  was 
inexhaustible. 

A  reminder  of  how  far  the  subject  still  is  from 
finality  comes,  as  the  last  pages  are  passing  through  the 
press,  in  the  announcement  by  Prof.  J.  J.  Thomson  of 
his  demonstration  that  iron  continues  to  be  strongly 
susceptible  to  magnetisation  by  such  rapid  alternations 
of  magnetic  force  as  occur  in  a  Leyden-jar  discharge ; 
and  that  the  damping-out  of  the  electric  oscillations 
when  the  discharge  traverses  a  coil  with  an  iron  core 
proves  magnetic  hysteresis  to  play  an  important  part, 
notwithstanding  the  excessive  frequency  of  the  reversals. 
Independent  experiments  made  by  Prof.  Trowbridge 
point  to  the  same  conclusion.  Prof.  Thomson's  use  of 
vacuum-globes  without  electrodes  as  induction  secon- 
daries opens  up  new  possibilities  of  magnetic  research, 
which  he  has  himself  been  the  first  to  turn  to  account. 

A2 


PREFACE 
TO     THE     THIRD     EDITION. 

IN  this  Edition  a  number  of  references  are  given 
to  advances  which  the  subject  has  made  since  the 
book  was  originally  published,  and  a  Chapter  is  added 
on  "  Practical  Magnetic  Testing." 

J.  A.  EWING. 

Cambridge,  rpoo. 


CONTENTS. 


CHAPTER  I.— INTRODUCTORY. 

SECTION.     PAGE. 

Introductory 1  ....  1 

Magnetic  Poles,  Axis,  and  Moment       . .         . .         . .            2  ....  2 

Magnetic  Field  and  Magnetic  Force            . .         . ,         . .       3  ....  3 

Lines  of  Magnetic  Force  . .         . .         . .         . .         . .            4  ....  4 

Uniform  Magnetic  Field        . .         . .         . .         . .         . .       5  ....  6 

Continuity  of  the  Magnetic  State           . .         . .         . .            6  ....  7 

Intensity  of  Magnetisation    . .         . .         . .         . ,         . .       7  ....  7 

Kelation  of  I  to  Pole- Strength 8  8 

King  Magnet 9  ....  8 

Lines  of  Magnetisation    ..         ..         ..         ..         ..        10-11  ....  9 

Magnetic  Force  within  the  Metal     . .         . .         ..  „         ..  12  ....  11 

Magnetic  Induction          . .         . .         . .         . .         . .  13  ....  12 

Distinction  between  Magnetic  Induction  and  Magnetic 

Force  within  the  Metal 14  ....  12 

Particular  Cases    . .         . .         . .         . .         . .         . .  15  ....  13 

Magnetic  Permeability           . .         . .         . .         . .         ..  16  ....  14 

Permeability  of  Paramagnetic  and  Diamagnetic  Substances  17  ....  16 

Illustrations  of  Permeability 18  ....  16 

Magnetic  Susceptibility        19  ....  18 

Connection  of  the  Ideas  of  Permeability  and  Susceptibility  20  ....  18 
Caution  with  regard  to  the  Use  of  the  Ideas  of  Perme- 
ability and  Susceptibility 21  ....  19 

Influence  of  the  Form  of  Bodies  on  the  Magnetisation 

induced  in  them 22  ....  20 

Long  Rod  placed  Lengthwise  in  a  Uniform  Field       . .  23  ....  21 

Analogy  of  Induced  Magnetisation  to  Electric  Conduction  24  ....  22 

Cases  in  which  the  Magnetisation  is  Uniform :  Ellipsoid  25  ....  23 

Magnetisation  of  an  Ellipsoid          26  ....  24 

Distribution  of  Free  Magnetism   in  a   Uniformly  Mag- 
netised Ellipsoid       27  ....  25 

Moment  of  Ellipsoid  . .         . .         . .         . .         . .      '   . .  28  . . . .  27 

Application  to  the  Case  of  a  Sphere 29  ....  27 

Application  to  the  Case  of  a  Short  Ellipsoid        . .         . .  80  ....  29 


Viil.  CONTENTS. 

SECTION.     PAGE. 

Application  to  the  Case  of  a  Long  Cylindrical  Eod  of  Cir- 
cular Section  Magnetised  Transversely  in  a  Uniform 

Field 31     ....     30 

Case  of  a  Thin  Disc  Magnetised  in  the  Direction  of  the 

Thickness  by  a  Uniform  Field 32     ....     31 

Long  Ellipsoid:   Influence  of  the  Length  on  the  Mag- 
netising Force          33     ....     31 

.Residual  Magnetism  and  Eotentiveness 34     ....     32 

Self-Demagnetising  Force  . .         . .         . .         . .          35     ....     33 

Self -Demagnetising  Force  in  Ellipsoids     . .         . .         . .     36     ....     34 


CHAPTER  II.  —  MEASUREMENTS  OF  MAGNETIC 
QUALITY:  THE  MAGNETOMETRIC  METHOD. 

SECTION.     PAGE. 
Methods  of  Measuring  Magnetic  Quality    . .         . .         . .     37     ....     35 

Classification  of  Methods  :  Magnetometrio  and  Ballistic        38     ....     36 

Magnetometric  Method 39-40..    37-39 

Details  of  Magnetometric  Method    , 41     ....     40 

Demagnetising  by  Eeversals       . .         . .         . .         . .          42     «...     46 

Adjustment  of  the  Current  required  to  balance  the  Ver- 
tical Component  of  the  Earth's  Field 43     ....     46 

To  find  the  Directing  Force  at  the  Magnetometer      . .          44     ....     47 
Example  of  a  Test  of  Iron  by  the  Magnetometric  Method    45     ....     49 

Magnetisation  Curve        46     ....     52 

Residual  Magnetism  and  Coercive  Force 47     ....     52 

Correction  of  the  foregoing  results  to  allow  for  the  Re- 

action  of  the  Specimen  on  the  Magnetising  Field  48     ....     54 

Differential  Susceptibility  and  Differential  Permeability. .     49     ....     56 
Supplementary  Remarks  on  the  Magnetometric  Method       50     ....    56 


CHAPTER    III.— MEASUREMENTS     OF    MAGNETIC 
QUALITY:   THE  BALLISTIC  METHOD. 

SECTION.     PAGE. 

The  Ballistic  Method 51     ...,  59 

Earth  Coil . .         . .          52     ....  60 

Use  of  a  Solenoid  and  Current  for  Standardising  the  Bal- 
listic Galvanometer        53     ....  62 

Damping  and  Calibration  of  the  Ballistic  Galvanometer       54     ....  63 

Ballistic  Tests  of  Rings  and  Rods          55     ....  64 

Calculation  of  B  from  Ballistic  Measurements     . .         . .     50     ....  66 

Magnetic  Force  in  Rings  . .         . .         . .         . .         . .          57     ....  66 

Bar  and  Yoke 58     67 

Hopkinson's  Application  of  the  Bar  and  Yoke            . .          59     ....  69 

Double  Bars  and  Yokes         60     69 

Example  of  the  Ballistic  Method          61     ....  70 


CONTENTS.  IX. 

CHAPTER  IV.— EXAMPLES  OF  MAGNETISATION. 

SECTION.     PAGE. 
Ballistic  Method  Using  Keversals :    Magnetisation  of  an 

Iron  King  (Eowland) 62  ....  73 

Cyclic  Process  of  Magnetisation :  Long  Iron  Wire     . .  63  ....  75 

Magnetisation  of  Iron  Hods  of  Various  Lengths    . .         . .  64  . . . ,  77 

Wrought-Iron  Bar  65     79 

Magnetisation  of  Mechanically  Hardened  Iron      . .         . .  66  ....  80 

Magnetic  Qualities  of  Steel         67  ....  82 

Magnetisation  of  Pianoforte  Steel  Wire 68  ....     83 

Cast  Iron    . .         . ,         . .  69     85 

Non-Magnetic  Steels 70     85 

Nickel         71  ....     86 

Cobalt 72  ....     88 

Curves  of  Permeability  and  Susceptibility       . .         . .  73  ....     88 

Susceptibility  Curves  for  Wrought-Iron  Wire        . .         . .  74  ....  88 

Permeability  Curves  for  Nickel..           75  ....  91 

Permeability  Curves  for  Cobalt 76  ....  92 


CHAPTER  V.— MAGNETIC  HYSTERESIS. 

SECTION.     PAGE. 

Magnetic  Hysteresis         77     ....     93 

Effects  of  Hysteresis 78     ....     94 

Dissipation  of  Energy  through  Magnetic  Hysteresis  . .  79     ....     99 

Heating  Effect  of  a  Cyclic  Process 80     102 

Values  of  fHd  I 81     ....  103 

Dissipation  of  Energy  by  JReversals  of  Moderately  Strong 

Magnetisation 82     ....  105 

Influence  of  Speed  on  Magnetic  Hysteresis     . .         . .  83     ....  108 

Steinmetz  Coefficient  of  Hysteresis  83A   111 

Effects  of  Vibration          84     ....  112 

Experiments  on  the-  Effects   of  Vibration  in  the  Mag- 
netisation of  Soft  Iron  Wire     85     ....  114 

Magnetic  Curve  Tracer 85A 118 


CHAPTER  VI.— MAGNETISM  IN  WEAK  FIELDS. 

SECTION,      PAGE. 

Permeability  with  respect  to  Small  Magnetic  Forces     . .     86     124 

Lord  Bayleigh's  Experiments    . .         . .         . .         . .  87     ....  126 

Magnetic  Viscosity  under  Small  Forces 88     ....  127 

Further  Experiments  on  Time  Lag  in   Magnetisation    89     ....  131 
Molecular  Accommodation  ..         .. 90    ...»  135 


CONTENTS. 


CHAPTER  VII— MAGNETISM  IN   STRONG  FIELDS. 

SECTION.  PAGE. 

Magnetisation  in  Strong  Fields 91  ....  136 

The  Isthmus  Method 92  ....  138 

Early  Experiments,  using  the  Isthmus  Method  . .  . .  93  ....  139 

Later  Experiments,  using  the  Isthmus  Method  . .  94  ....  143 
Theory  of  the  Isthmus  Method  :  Form  of  Cone  to  give 

Maximum  Concentration  95  ....  145 

Greatest  Magnetising  Force  producible  by  means  of  Cones  96  ....  147 

Form  of  Cone  to  give  most  Uniform  Field  . .  , .  97  ....  148 

Further  Experiments  with  Wrought  Iron  ..  ..  98  ....  150 

Cast  Iron  and  Steel  in  very  Strong  Fields  . .  . .  99  151 

Hadfield's  Manganese  Steel  in  Strong  Fields       . .         . .  100  ....  153 

Nickel  and  Cobalt  in  Strong  Fields     . .         . .         . .  101  ....  153 

Summary  of  Conclusions  from  Isthmus  Experiments   . .  102  ....  155 

Apparatus  for  applying  the  Isthmus  Method. .         . .  103  ....  156 

Experiments  by  Du  Bois  -with  Strong  Fields.  Optical 

Method 104  ....  158 

Eesults  of  Optical  Measurements  105  ....  161 

Magnetisation  of  Magnetite  106  162 

Experiments  with  Ellipsoids 107  ....  163 


CHAPTER  VIII.— EFFECTS  OF  TEMPERATURE. 

SECTION.       PAGE. 
Effects  of  Temperature  on  Magnetic  Quality :    Loss  of 

Magnetic  Quality  at  a  High  Temperature    . .         . .  108  ....  1^6 

Change  of  Physical  State  at  the  Critical  Temperature  109  ....  167 

Effects  of  Temperature  Below  the  Critical  Point      . .         110  ....  168 
Hopkinsnn's  Experiments  on  the  Magnetisation  of  Iron 

at  Various  Temperatures        Ill  ....  170 

Whitworth's  Mild  Steel 112  173 

Whitworth's  Hard  Steel 113  ....  174 

Hopkinson's  Experiments  with  Nickel  . .         . .         114  ....  175 

Effects  of  Temperature  within  the  Atmospheric  Eange  115  ....  178 
Effects  of  Varying  Temperature,  the  Magnetic    Force 

being  Constant 116  ....  180 

Experiments  in  Alternate  Heating  and  Cooling  of  Mag- 
netised Iron 117  ....  181 

Hysteresis  in  the  Kelation  of  Magnetic  Susceptibility  to 

Temperature  118  ....  184 

Hopkinson's  Experiments  with  Nickel-Iron  Alloys        . .  119  ....  186 

Eesearches  on  Effects  of  Temperature  by  Dr.  Morris        119A  ....  190 
"Ageing"  of  Iron  by  Prolonged  Exposure  to  Moderate 

Temperature 119u  ....  193 


CONTENTS.  ft 


CHAPTER  IX.— EFFECTS  OF  STEESS. 

SECTION.       PAGE. 

Effects  of  Stress :  Introductory 120  ....  197 

Effects  of  Longitudinal  Pull  on  the  Susceptibility  and 

Retentiveness  of  Nickel      . .          . .         . .         . .         121  ....  193 

Effects  of  Longitudinal  Push  on  the  Susceptibility  and 

Retentiveness  of  Nickel          . .         . .         . .         . .  122  ....  202 

Effects  of  Cyclic  Variation  of  Longitudinal  Stress  on  the 

Magnetism  of  Nickel          ..         -^         ..         ..         123  ....  206 

Effects  of  Longitudinal  Pull  in  Iron         124  ....  209 

Annealed  Iron  under  Pulling  Stress   . .         . .         . ,         125  ....  209 

Hardened  Iron  under  Pulling  Stress         , .         . .         . .  126  ....  212 

Effects  of  Applying  Longitudinal  Pull  to  Magnetised  Iron  127  216 

Hysteresis  in  the  Effects  of  Stress       . .         . .         . .         128  ....  219 

Influence  of  Vibration  on  the  Effects  of  Stress  . .         . .  129  ....  222 

Effects  of  Loading  Annealed  Iron       . .         . .         ..         130  222 

Effects  of  Longitudinal  Stress  in  Cobalt 131  ....  222 

Kelation  between  the  Effects  of  Stress  on  Magnetism, 
and  the  Effects  of    Magnetism   in  changing   the 

Dimensions  of  Magnetic  Metals  . .         . .         . .         132  ....  224 

Residual  Effects  of  Stress  applied  before  Magnetising  . .  133  ....  225 

Experiments  showing  Residual  Effects  of  Stress      . .         134  , . . .  226 

Other  Evidences  of  Hysteresis  in  the  Effects  of  Stress. .   135  ....  230 

Effects  of  Torsion  on  Magnetic  Quality         . .          . .         136  231 

Effects  of  Torsion  due  to  Magnetic  Aeolotropy  ..         ..  137  ....  232 

Production  of  Longitudinal  Magnetism  by  Twisting  a 

Circularly  Magnetised  Wire         . .         . .         . .         138  ....  234 

Torsional  Strain  Produced  by  Combining  Circular  with 

Longitudinal  Magnetisation    . .         . .         . .         . .  139  ....  236 

Transient  Currents  produced  by  Magnetising  Twisted 

Rods,  or  by  Twisting  Magnetised  Rods  ..         ..         110  ....  237 

Effects  of  Combined  Pull  and  Torsion  on  the  Magnetisa- 
tion of  Iron  and  Nickel            141  240 

Effects  of  Cyclic  Twisting  in  Nickel,  when  Associated 

•with  Longitudinal  Pull 142  244 

Strain  caused  by  Magnetisation 143  ....  249 

Modification  of  the  Results  by  applying  Tensile  Stress        144  ....  252 

Stress  due  to  Magnetisation           . .         . .         . .          . .   145  ....  254 

Tractive  Force  in  Divided  Magnets     . .         . .          . .         146  ....  254 

Relation  of  Tractive  Force  to  Magnetisation      . .          . .   147  ....  257 

Determination     of    Magnetisation    by    Measuring    the 

Tractive  Force         148  ....  259 


CONTENTS. 


CHAPTEB  X.— THE  MAGNETIC  CIRCUIT. 

SECTION.       PAGE. 

The  Magnetic  Circuit          149  ....  262 

Tubes  of  Magnetic  Induction.    Definition  of  Magnetic 

Flux  and  of  a  Perfect  Magnetic  Circuit  . .         . .         150  ....  263 

Imperfect  Magnetic  Circuit ..         ..         ..         ..          ..  151  ....  265 

Line-Integral  of  Magnetic  Force,  or  Magnetomotive  Force  152  ....  265 

Value  of  the  Line-Integral  of  Magnetic  Force     . .         . .  153  ....  266 

Equation  of  the  Magnetic  Circuit        154  ....  268 

Particular   Cases :    Continuous  Ring  wound  uniformly 

and  otherwise . .   155  ....  271 

King  Magnet  with  an  Air  Gap . .          156  ....  275 

Comparison  of  a  Split-King  with  an  Ellipsoid    . .         . .   157  ....  276 
Graphic  Kepresentation  of  the  Influence  of  a  Narrow  Gap  158  ....  278 
Graphic  Representation  of  the  relation  of  Flux  to  Mag- 
netomotive Force    . .         . .         . .         . .         . .         159  ....  280 

Application  to  Dynamos 160  ....  282 

Bar  and  Yoke 161  ....  283 

Magnetic  Resistance  of  Joints        162  ....  285 

Calculation  of  the  Equivalent  Air-Gap          . .         . .         163  ....  287 
Influence  of  Compression  on  the  Magnetic  Resistance  of 

a  Joint 164  ....  289 

Experiments  with  Rough  Joints         . .         ...       . .        165  ....  2'Jl 


CHAPTER  XI.— MOLECULAR  THEORY. 

SECTION.       PAGE. 

Molecular  Theories :  Poissou  and^  Weber 166  ....  291 

Experimental  Evidence  in  Favour  of  Weber's  Theory 

from  the  Facts  of  Saturation,  &c 167  295 

Constraint  of  the  Molecular  Magnets  in  Weber's  Theory  168  ....  297 

Maxwell's  Modification  of  Weber's  Hypothesis  ..         ..169  ....  298 
Hypothesis  of  Frictional  Resistance  to  the  Deflection  of 

the  Molecules 170  ....  298 

The  Constraint  of  the  Molecules  due  to  their  Mutual 

Action  as  Magnets ..        171  299 

Imaginary  Molecular  Groups.— A  Single  Pair    . .         . .  172  ....  301 

Group  of  Four  Members           173  307 

Continuous  Distribution  in  Cubical  Order          . .         . .  174  ....  310 
Agreement  of  the  Theory  with  known  Facts  about  Sus- 
ceptibility             175  ....  313 

Retentiveness  and  Residual  Magnetism 176  ....  314 

Experiments  on  Residual  Magnetism  in  Iron           . .         177  .  *  • .  316 

Retentiveness  of  Nickel 178  •--•  323 


CONTENTS.  Xlii. 
SECTION.        PAGE. 
Amount  of  Ketentiveness  possible  under  the  Molecular 

Theory         179  ....     323 

Hysteresis  and  the  Dissipation  of  Energy          . .         . .  180  ....     326 
Eotation   in     a     Magnetic    Field.     Disappearance    of 

Hysteresis  when  the  Field  is  strong       ..         ..         181     326 

Reduction  of  Hysteresis  by  Vibration  and  other  Dis- 
turbances             182  ....     329 

The  Molecular  Theory  and  the  Effects  of  Temperature     183     333 

Time-Lag  in  Magnetisation    . .         . .         . .         . .           18 1  ....     334 

Effects  of  Permanent  Mechanical  Strain. .         ..         ..185  ....     335 

Effects  of  Eepetition  of  Magnetic  Processes..         ..         186  ....     337 

Effects  of  Elastic  Strain 187  ....     343 

Hysteresis  in  Changes  of  Molecular  Configuration,  apart 

from  the  Existence  of  Magnetisation     . .         . .         188  ....     347 
Experimental  Study  of  Molecular  Groups  by  means  of 

Models 189  ....     348 

Ampere's  Hypothesis  as  to  the  Nature  of  the  Magnetic 

Molecules                                                                     190  ....     352 


CHAPTER  XII.— PRACTICAL  MAGNETIC  TESTING. 

SECTION.        PAGE. 

Practical  Magnetic  Tests 191     355 

The  Ballistic  Method 192     356 

Form  of  Specimens  for  Ballistic  Te?ts 193     360 

Use  of  Double  Bars  and  Yokes  194       ...     362 

Permeability  Briage 195     ....     366 

Apparatus  using  a  Yoke  with  a  Gap    . .         . .         . .         196     ....     372 

Du  Bois'  Magnetic  Balance 197     ....     374 

The  Author's  Magnetic  Balance          198     375 

Hysteresis  Tester 199     ....     378 


INDEX 385 


LIST  OF  ILLUSTRATIONS. 


Fio.  PAGE. 

1  Force  due  to  Magnetic  Poles    . .         . .         . «         • »         •  •  4 

2  Lines  of  Force  due  to  Two  Poles 5 

3  Magnetic  Field  Bound  a  Bar  Magnet 5 

4  Lines  of  Magnetisation  in  a  Magnetised  Bing    . .         . .  10 
fi       Disturbance  of  an  Originally  Uniform  Magnetic  Field  by 

the  Introduction  of  a  Soft  Iron  Sphere 17 

8  Disturbance  of  an  Originally  Uniform  Magnetic  Field  by 

the  Introduction  of  a  Sphere  of  Strongly  Diamagnetic 

Material 17 

7-8  Uniformly  Magnetised  Ellipsoids  25 

9-10  Distribution  of  Free  Magnetism  in  a  Uniformly  Magnetised 

Ellipsoid 26 

11  Short  Ellipsoid  of  Infinitely  Permeable  Material  in  an 

Originally  Uniform  Field . .  29 

12-13  Deflection  of  a  Magnetometer  Needle  38 

14  "  One-Pole "  Method  of  using  the  Magnetometer     ..         ..40 

15  Mirror  Magnetometer          41 

16  Arrangement  for  Examining  Magnetic  Quality  by  means  of 

the  Magnetometer      . .         . .         . .         . .         . .         . .  43 

17  Liquid  Bheostat 45 

18  Diagram  of  Connections  in  Magnetometric  Experiments    . .  45 

19  Magnetic  Force  Due  to  a  Circular  Coil 49 

20  Curve  of  Magnetisation  in  Annealed  Wrought  Iron. .         . .  53 

21  Curve  Distorted  by  using  a  Compensating  Coil  . .         . .  57 

22  Earth  Coil  for  use  in  Ballistic  Measurements          . .         . .  61 

23  Diagram  of  Connections  for  Ballistic  Method     . .         . .  64 
24-25    Bings  for  Ballistic  Tests          . .         , 67 

26  Yoke  and  Bar  for  Ballistic  Tests  ..         ...         ..         ..  68 

27  Hopkinson's  Yoke  and  Bar 69 

28  Yoke  with  Double  Bars 70 

29  Curve  of  Magnetisation  of  a  Wrought-Iron  Bing     . .         . .  72 

80  Induced  and  Besidual  Magnetism  in  a  Wrought-Iron  King 

(Bowland)              75 

81  Magnetisation  of  a  Soft  Iron  Wire 76 

32  Magnetisation  of  Soft  Iron  Bods  of  Various  Lengths    . .  78 

33  Magnetisation  of  a  Wrought-Iron  Bar  in  a  Yoke  (Hopki»*on)  80 

34  Cyclic  Magnetisation  of  Soft  Iron  Wire         81 

35-36    Cyclic  Magnetisation  of  Pianoforte   Steel,  Annealed  and 

Glass-Hard            84 

37      Magnetisation  of  Cast-Iron  (Hopkinson) 85 


vJ.  LIST    OF    ILLUSTRATIONS. 

FIG.  PAGE. 

38  Cyclic  Magnetisation  of  Nickel  Wire 87 

39  Cyclic  Magnetisation  of  Cobalt          89 

40  Curves  of  Magnetic  Susceptibility  in  Soft  and  Hard  Iron  90 

41  Curves  of  Permeability  in  Nickel      . .          . .          . .         . .  91 

42  Curves  of  Permeability  in  Cobalt            92 

43  Illustration  of  Hysteresis  in  the  Magnetisation  of  a  Soft 

Iron  King 95 

44  Hysteresis  in  the  Kemoval  and  Ke-application  of  Magnetic 

Force  in  Soft  Iron          96 

45  Influence  of  Previous  Magnetisation           98 

46-49   Work  Done  in  Magnetising          100-102 

50  Graded  Cyclic  Magnetisation  of  Soft  Iron 106 

51  Curve  of  Energy  Dissipated  in  Reversals  of  Magnetism  in 

Soft  Iron 107 

52  Cyclic  Reversals  in  Steel        109 

53  Heating  Effect  of  Reversals  in  Iron  and  Steel. .         . .  110 
54-55    Magnetisation  of  Soft  Iron  with  and  without  Vibration    115-116 

56      Effects  of  Tapping  at  Points  in  the  Magnetising  Process  117 

56A    Magnetic  Curve-Tracer           118 

56s    General  Arrangement  of  Curve-Tracer 119 

56c     Cyclic  Process  recorded  by  Magnetic  Curve-Tracer          . .  120 

56o     Cyclic  Process  with  Subordinate  Loops            . .         . .  120 

56s    Cyclic  Process  at  Various  Speeds 121 

56F    Cyclic  Processes  in  Iron  and  Steel          122 

56a    Cyclic  Curves  with  Graded  Limits  of  Magnetising  Current  123 

57      Magnetic  Lag  in  Very  Weak  Fields 129 

58-59    Influence  of  Time  in  the  Magnetisation  of  Soft  Iron  by 

Weak  Forces        130 

60  Effects  of  Steps  in  the  Magnetising  Process           . .         . .  131 

61  Diagram  Showing  Lagging  in  a  Step 132 

62  Influence  of  Time  in  the  Performance  of  a  Small  Cyclic 

Process           133 

63  Curve  of  Permeability  in  Strong  Fields  (Bidwell)        . .  138 
64-65    The  Isthmus  Method  of  testing  the  Effects  of   Strong 

Fields 140 

66  Curves  of  Permeability  of  Cast  and  Wrought-Iron  in  very 

S-rong  Fields 143 

67  Application  of  the  Isthmus  Method             . .         . .         . .  144 

68  Concentration  of  Magnetic  Force  by  Cones       . .         . .  146 

69  Form  of  Cones  giving  Maximum  Concentration     .  •         . .  149 

70  Form  of  Cones  giving  most  Uniform  Field       . .         . .  149 

7  L      Sections  of  Cones  and  Bobbins          151 

72      Curves  of  Permeability  of  Wrought  Iron,  Steel,  Cast  Iron, 

Nickel,  Cobalt,  and    Manganese  Steel  in  very  Strong 

Fields 155 

73-74    Electromagnet   and  Turning    Bobbin    for    the    Isthmus 

Method 157 

75      Optical  Method  of  Measuring  Magnetism  in  Strong  Fields 

(DuBois)       ...        160 


LIST   OF    ILLUSTRATIONS.  Xvii. 

Fio.  PAGE. 

76      Magnetisation  Curve  of  Iron,  Nickel,  and  Cobalt        . .          163 

77-78    Magnetisation  Curves  of  Iron  at  Various  Temperatures 

(Hopkinson) 171 

79      Eelation  of  Permeability  to  Temperature  in  Iron,  under  a 

Weak  Magnetising  Force  ( Hopkinson)  ..         ..          172 

80-81     The  same  under  Stronger  Forces 173 

82-83    Magnetisation  of  Mild  Stoel    at  Various    Temperatures 

(Hopkinson)         174 

84-85    Magnetisation  of  liard  Steel  at  Various  Temperatures 

(Hopkinson) 175 

86-87    Magnetisation  of  Nickel  at  Various  Temperatures  (Hop- 
kinson)               176-177 

88  Effects  of  Heating  to  100°C.  on  the  Magnetic  Susceptibility 

of  Soft  and  Hard  Iron         179 

89  Effect  of  Heating  and  Cooling  a  Steel  Bar  Magnet      . .          183 
90-94     Hopkinson's  Experiments  with  Nickel  Steel          . .         186-189 

94A  Effects  of  Temperature  on  the  Permeability  of  Iron  (Morris)  191 

94s  Record  of  the  Cooling  of  Iron  (Roberts  Austen)          . .  192 

94o  Effects  of  Baking  on  the  Hysteresis  of  Sheet  Iron  (Roget)  194 

94D  Effects  of  Baking  on  the  Permeability  of  Sheet  Iron  (Roget)  196 

95  Magnetisation  of  Annealed  Nickel  under  Various  Amounts 

of  Longitudinal  Pull 200 

96  The  same  for  Hard-Drawn  Nickel 201 

97  Apparatus  for  Testing  Metals  under  Compression       . .  203 

98  Curves  of  Induced  Magnetism  of  Nickel  under  Longitudinal 

Compression..         ..         ..         ..         ..         ..         ..     204 

99  Curves  of  Residual  Magnetism  of  Nickel  under  Longi- 

tudinal Compression      . .         . .         . .         . .         . .  205 

100  Curves  of  Permeability  of  Nickel  under  Compression       . .     206 

101  Curves  of  Induced  and  Residual  Magnetism  of  Annealed 

Nickel  under  Compression        207 

102  Effects  of  Loading  and  Unloading  Nickel  Wire  in  Various 

Constant  Fields         208 

103-104  Curve  of  Magnetisation  of  Annealed  Iron  under  Longi- 
tudinal Pull        ..         ..         210-211 

105-107  Curve  of  Magnetisation  of  Hard  Iron  under  Longitudinal 

Pull 213-215 

108-111   Effects  of  Applying  and  Removing  Loads  on  Magnetised 

Iron  Wires  . .         . .         . .         . .         . .         . .    218-221 

112  Effect  of  Compressive  Stress  in  Cobalt        . .         . .         . .     223 

113  Magnetisation  Curves  of  Iron,  showing  Residual  Effects 

of  Previous  Loads          . .         . .         . .         . .         . .  229 

114  Effects  of  Twist  in  Iron          232 

115  Development  of  Aeolotropy  by  Twist 233 

116  Production  of  Longitudinal  Magnetisation  by  Twisting  a 

Circularly  Magnetised  Rod 235 

117  Curves  of  Circular  Magnetisation  produced  by  Twisting 

Longitudinally  Magnetised  Iron         237 

118-119  The  same  in  Steel       238-239 


LIST    OF    ILLUSTRATIONS. 

Fio.  PAGE. 

120  Magnetisation  of  Nickel  under  Torsion  (Nagaoka)      . .          242 

121  Magnetisation  of  Nickel  under  combined  Pull  and  Torsion     243 
122-124  Effects  of  Cyclic  Twisting  in  Magnetised  Nickel  (Nagaoka)  246-248 

125      Apparatus  for  determining  the  Change  of  Length  caused 

by  Magnetisation  (Bidwell) 250 

126-1 27   Curves  showing  Changes  of  Length  due  to  Magnetisation  in 

Iron,  Nickel,  and  Cobalt  (Bidwell; 252 

128  The  same  for  Iron  under  Longitudinal  Pull  . .         . .     253 

129  Apparatus  for  Measuring  Magnetic  Tractive  Force  (Bosan- 

quet)          256 

130  S.  P.  Thompson's  Permeameter        261 

131  Example  of  an  Imperfect  Magnetic  Circuit       . .         . .  273 

132  Graphic  Treatment  of  an  Air  Gap  in  the  Magnetic  Circuit  279 

133  Graphic  Treatment  of  a  Composite  Circuit  . .         . .  281 

134  Influence  of  a  Smooth  Joint  on  the  Magnetic  Eesistance 

of  an  Iron  Bar    . .         , 288 

135  Effects  of  Successive  Cuts  in  a  Bar 292 

136  The  Three  Stages  of  the  Magnetising  Process  . .         . .  300 
137-140  Deflection  of  a  Pair  of  Magnetic  Molecules  by  Application 

of  an  External  Field  301-304 

141-143   Deflection  of  a  Group  of  Four  Magnetic  Molecules     . .   307-308 
144       Curve  of  the  Eesultant  Moment  of  the  Group      .  .         . .     309 

145-147  Deflection  of  a  Multiform  Group 310-312 

148       Curves  of  Induced  and  Residual  Magnetism  in  Iron,  in 

the  Soft  State,  and  Hardened  by  Stretching       . .          . .     317 
149-151   Proportion  of  Eesidual  to  Induced  Magnetism  in  Iron  318-322 
15lA    Hysteresis  in  Alternating  and  Eotating  Fields  (Baily)      . .     328 
152-153   Influence  of  an  Alternating  Electric  Current  in  Iron  Wire 

during  Magnetisation  (Gerosa  and  Finzi) . .         . .        331-332 

154  Eepetition  of  Magnetic  Cycles  in  Iron 311 

155  Cyclic  Force  in  Iron  previously  Demagnetised  by  Reversals     342 

156  Repetition  of  Magnetic  Cycles  in  Steel        344 

157  Effects  of  Eepeated  Loading  on  an  Iron  Wire  in  a  Weak  Field    346 

158  Pivoted  Magnet  used  in  Construction  of  Model  to  Illustrate 

the  Molecular  Theory          348 

158A     General  Arrangement  of  Model  . .         . .         . .          . .  350 

159  Curve    of  Cyclic  Process  applied  to  a  Group  of  Pivoted 

Magnets          351 

160  Arrangement  for  Ballistic  Tests 357 

161  Cyclic  Processes  by  Ballistic  Method  360 

162-3    Double  Bars  and  Yokes     . .         « 362 

164  Method  of  Correcting  for  Yokes        365 

165  General  View  of  Permeability  Bridge 366 

166  Details  of  Permeability  Bridge          368 

167  Example  of  Curve  by  Permeability  Bridge       . .         . .  371 
168-9  Koepsel's  Apparatus 372-373 

170-171  Du  Bois' Magnetic  Balance          374-375 

172 ^  The  Author's  Magnetic  Balance        377 

173      Hysteresis  Tester    . .         . . 380 


CHAPTER  L 


INTRODUCTORY. 

§  1.  Introductory. — Though  all  substances  show  some  mag- 
netic quality,  there  are  three  that  form  a  group  distinct  from 
all  others  in  this  respect.  In  other  metals  and  non-metals  a 
feeble  magnetisation  may  be  induced  with  difficulty ;  iron, 
nickel  and  cobalt  take  magnetism  readily,  and  take  it  in 
amounts  that  are  relatively  enormous.  In  other  substances  we 
have  no  evidence  that  there  is  such  a  thing  as  permanent 
magnetism,  but  these  three  can  retain  magnetism  strongly. 
Their  capability  of  being  magnetised,  which  is  more  or  less  shared 
by  alloys  in  which  one  or  other  of  them  is  contained  (and  also 
by  the  magnetic  oxide  of  iron),  is  so  conspicuously  great,  in 
comparison  with  that  of  any  other  substance,  that  they  may 
properly  be  said  to  stand  apart  as  the  magnetic  family  of 
metals.  Our  purpose  is  to  give  some  account  of  the  properties 
that  entitle  them  to  this  name. 

Before  proceeding  to  speak  of  experiments  and  their  results, 
it  may  be  well  to  recall  the  various  conventions  according  to 
which  magnetic  quantities  are  expressed.  Most  of  this  intro- 
ductory matter  is,  of  course,  familiar  to  the  student,  but  parts 
of  it,  perhaps,  are  less  familiar,  and  some  confusion  is  apt  to  be 
felt  on  account  of  the  variety  of  ways  which  one  may  follow  in 
stating  facts  about  magnetic  quality.  The  magnetisation  of  an 
iron  bar,  for  example,  maybe  specified  by  its  magnetic  moment, 
by  its  intensity  of  magnetisation,  or  by  its  magnetic  induction ; 
and  its  readiness  to  be  magnetised  may  be  measured  either 
by  what  is  called  its  magnetic  permeability,  or  by  another 
not  quite  identical  quantity  called  its  magnetic  suscepti- 
bility. The  student  is  liable  to  feel  that  there  is  an  embarras 


2  MAGNETISM    IN   IRON. 

de  rickesse  in  magnetic  ideas  and  phraseology.  The  various 
lights  in  which  the  magnetism  of  a  piece  and  its  magnetic 
quality  may  be  regarded  are,  of  course,  consistent  with  one 
another,  and  are  related  in  a  simple  enough  manner.  Some  forms 
of  expression  have  the  advantage  that  they  fit  in  best  with 
modern  conceptions  of  the  magnetic  state;  others  survive  because 
they  are  more  convenient  in  special  cases.  The  magnetic  circuit 
of  a  dynamo  is  most  simply  treated  by  using  one  set  of  terms ; 
another  set  of  terms  come  readier  to  hand  when  we  have  to 
speak  about  the  properties  of  a  magnetised  steel  bar.  The 
student  will,  therefore,  do  well  to  master  the  meaning  of  all  the 
magnetic  terms  in  common  use,  and  should  accustom  himself 
to  look  at  magnetic  phenomena  from  various  points  of  view. 

§  2.  Magnetic  Poles,  Axis,  and  Moment. — An  old  and  still 
useful  way  of  looking  at  the  matter  is  to  think  of  the  action  of 
a  magnet  as  due  to  the  existence  of  two  quantities  of  hypothetical 
magnetic  substance,  or  "  free  magnetism,"  equal  in  amount  and 
opposite  in  kind,  which  are  distributed  in  the  neighbourhood 
of  the  two  ends.  These  hypothetical  positive  and  negative 
substances  have  the  property  that  two  portions  of  like  kind 
repel  each  other,  and  two  portions  of  unlike  kind  attract  each 
other,  with  a  force  which  is  proportional  to  the  product  of  the 
amounts  of  the  substances,  and  inversely  proportional  to  the 
square  of  the  distance  between  them.  In  an  ordinary  bar 
magnet  the  free  magnetism  is  distributed  partly  over  the 
surface  at  and  near  the  ends  of  the  bar,  and  partly  throughout 
the  interior  of  the  bar,  especially  near  the  ends.  The  action  of  the 
magnet  upon  anything  at  a  considerable  distance  from  it  is  much 
the  same  as  it  would  be  if  the  free  magnetism  were  concen- 
trated at  two  points,  near  the  ends,  which  are  called  the  poles. 
Strictly  speaking,  there  are  no  precise  poles  in  a  magnet — that 
is  to  say,  there  are  no  two  points  at  which  we  might  imagine 
the  positive  and  negative  free  magnetism  to  be  gathered,  and 
find  the  magnetic  action  on  external  things  to  be  quite  un- 
changed. It  is  only  when  the  bar  is  very  thin  and  uniformly 
magnetised  (§  7,  below)  that  we  come  near  to  realising  the  idea 
of  two  definite  centres  of  force  at  the  ends  of  the  bar  where 
the  positive  and  negative  free  magnetism  is  concentrated.  The 
idea  of  poles  in  a  magnet  has  therefore  to  be  employed  with 


MAGNETIC  FIELD   AND   MAGNETIC   FORCE.  3 

much  caution,   but  it   is  too   useful  to  be  altogether  aban- 
doned. 

The  strength  of  a  pole  is  the  whole  amount  of  magnetism 
which  is  to  be  taken  as  gathered  there.  Unit  pole,  or  unit 
quantity  of  free  magnetism,  is  that  quantity  which  repels  or 
attracts  another  quantity  equal  to  itself  with  unit  force  when 
the  two  are  placed  at  unit  distance  from  each  other.  It  is 
now  a  universal  practice  to  express  magnetic  quantities  in 
terms  of  the  centimetre-gramme-second  system  of  units.  We 
may,  therefore,  define  the  unit  pole  as  that  which  acts  on 
another  pole  of  equal  strength  with  a  force  of  one  dyne  when 
the  two  are  placed  one  centimetre  apart.  The  axis  of  a  magnet 
is  the  line  joining  its  poles.  The  moment  of  a  magnet  is  its 
pole-strength  multiplied  by  the  distance  between  the  poles. 
According  to  this  conception  of  a  magnet,  the  magnetic  action 
of  the  bar  is  due  to  the  free  magnetism  at  the  poles ;  the 
middle  portion  of  it  is  neutral,  and  merely  serves  to  hold 
apart  the  ends,  in  which  the  free  magnetism  resides. 

§  3.  Magnetic  Field  and  Magnetic  Force. — For  many  purposes 
this  conception  of  poles  is  a  very  serviceable  one.  It  is  especially 
serviceable  when  we  have  to  treat  of  the  influence  which  the 
magnet  exerts  throughout  the  space  in  its  neighbourhood,  or 
throughout  what  is  called  the  magnetic  field.  To  examine  the 
magnetic  field,  we  may  think  of  the  force  which  the  magnet  N  S 
(Fig.  1)  will  exert  on  an  imaginary  particle  of  magnetic  sub- 
stance, P,  placed  anywhere  in  its  neighbourhood.  The  two 
poles  of  the  magnet  will  exert  two  forces,  F1  and  F2,  which  are 

proportional  to  and  :  one  pole  will  tend  to  pull 

the  particle  towards  it,  the  other  pole  will  tend  to  push  the 
particle  from  it.  These  forces  will  have  for  their  resultant  a 
single  force,  R,  which  is  the  whole  force  exerted  by  the  magnet 
upon  the  particle.  The  direction  of  this  resultant  is  definite 
at  any  point  in  the  field,  but  its  amount  will  depend  on  the 
amount  of  magnetic  substance  in  the  particle.  Suppose,  now, 
that  we  take  a  particle  in  which  the  amount  of  magnetic  sub- 
stance is  one  unit  (as  defined  in  §  2),  and  observe  the  force 
exerted  upon  it  when  it  is  placed  anywhere  in  the  field,  we 
now  find  a  force  which  is  definite  (at  any  one  point  of  the 

B2 


£  MAGNETISM    IN    IRON. 

field)  both  in  magnitude  and  direction.  This  force  measmns 
the  intensity  of  the  field  at  the  point  in  question,  and  is  called 
the  magnetic  force  at  that  point.  Instead  of  one  magnet  only 
there  may  be  any  number  of  magnets,  the  poles  of  which  con- 
tribute to  the  production  of  magnetic  force  at  any  point  of  the 
field  in  which  the  magnets  lie.  We  may  still  think  of  each  pole 
as  exerting  its  own  component  of  force  on  the  imaginary  par- 
ticle of  unit  strength,  and  then  combine  all  these  componenta 
to  find  a  single  resultant  which  measures  the  magnetic  force. 

Electric  currents  also  give  rise  to  magnetic  force  in  their 
neighbourhood,  so  that,  in  considering  the  value  of  the  mag- 
netic force  at  any  place,  we  have  to  take  their  action  into 


Fia.  L 

account  as  well  as  the  action  of  the  poles  of  neighbouring 
magnets.  But  whatever  currents  or  magnets  contribute  to  the 
production  of  the  magnetic  field,  the  magnetic  force  at  any 
point  of  space  has  a  definite  direction  and  value,  which  may 
be  expressed  by  stating  the  mechanical  force  which  would  be 
felt  by  a  unit  magnetic  pole  when  placed  there.  The  direction 
of  the  magnetic  force  is  the  direction  in  which  the  unit  particle 
will  tend  to  move,  and  the  value  of  the  magnetic  force  is  the 
value  in  dynes  of  the  mechanical  force  which  tends  to  move 
the  particle. 

§  4.  Lines  of  Magnetic  Force. — If  we  allow  the  particle  to 
move  so  that  the  direction  it  takes  is,  at  every  instant,  the 


OF  THE 

UNIVERSITY  ] 

OF 


LINES   OF   MAGNETIC   PORCH. 


direction  in  which  the  magnetic  force  acts  upon  it,  and  if  we 
mark  the  course  it  takes  through  space,  we  shall  trace  out  what 
is  called  a  line,  of  magnetic  force.  In  general  these  lines  are 
curved,  for  the  direction  of  the  magnetic  force  varies  as 


FIQ.  2. 


we  pass  from  point  to  point  through  the  field.  If  the 
magnetic  field  is  produced  by  a  single  pair  of  opposite 
poles,  the  lines  of  force  start  from  the  positive  pole  and 
spread  in  curves,  which  bend  round  through  space,  and  all 


Fio.  3, 

converge  on  the  negative  pole  (Fig.  2).  The  well-known  curves 
in  which  iron  filings  group  themselves  when  scattered  near 
a  magnet  represent  approximately  the  forms  taken  by  the 
lines  of  force.  In  the  field  produced  by  an  actual  bar  magnet 
(Fig.  3)  the  lines  do  not  converge  as  in  Fig.  2  to  a  single  pair 


6  MAGNETISM   IN    IRON. 

of  points,  for  the  positive  and  negative  quantities  of  free  mag 
netism  are  each  distributed  over  a  considerable  part  of  the 
length  of  the  bar.  Where  the  lines  come  close  to  one  another 
the  magnetic  force  is  intense :  where  they  lie  far  apart  the 
field  is  weak.  If  we  pass  along  lines  of  force  from  one  place 
to  another  in  the  magnetic  field,  we  shall  find  that  the  in- 
tensity of  magnetic  force  at  each  place  is  proportional  to 
the  number  of  lines  of  force  which  cross  an  imaginary  sur- 
face of  unit  area,  placed  there  and  set  so  that  it  stands  at 
right  angles  to  the  direction  of  the  lines.  We  can  make  the 
number  of  lines  which  cut  such  a  surface  not  only  propor- 
tional, but  numerically  equal  to  the  magnetic  force,  through- 
out the  whole  field,  by  adhering  to  a  proper  convention  as  to 
the  whole  number  of  lines  to  be  drawn.  The  convention  is 
that  the  number  of  lines  of  force  which  start  from  any  pole  of 
strength  m  is  4:irm.  Consider  a  sphere  of  radius  r  in  centi- 
metres enclosing  a  magnetic  pole  of  strength  m.  According  to 
the  convention,  the  number  of  lines  of  force  which  radiate  from 
the  pole  and  cut  the  surface  of  the  sphere  is  4:irm.  But  the 
area  of  surface  of  the  sphere  is  in  square  centimetres  47rr2. 
The  number  of  lines  of  force  per  square  centimetre  at  the 

surface  of  the  sphere  is  therefore or  — ,  and  this  is  also 

4  TT  r2       r2 

the  measure  of  the  magnetic  force  there,  for  the  force  is  due  to 
a  pole  ?7i  at  a  distance  r. 

§  5.  Uniform  Magnetic  Field. — In  a  uniform  field — that  is  to 
say,  a  field  in  which  the  magnetic  force  has  the  same  direction 
and  the  same  intensity  at  all  points — the  lines  of  force  are 
straight,  parallel,  and  equally  spaced.  The  magnetic  field  due 
to  the  earth's  action  as  a  magnet  is  sensibly  uniform  throughout 
any  small  space,  such  as  that  of  a  room.  Good  approximations 
to  a  uniform  field  can  be  obtained  by  suitable  arrangements  of 
magnets,  or  of  conductors  carrying  electric  currents.  Thus,  if 
we  take  a  long  uniform  solenoid  or  helix  of  wire,  wound  so  that 
the  diameter  is  constant  and  the  number  of  turns  is  the  same  in 
each  unit  of  the  length,  and  pass  a  current  through  it,  a  magnetic 
field  will  be  produced  which  is  very  nearly  uniform  throughout  the 
whole  space  within  the  solenoid,  except  close  to  the  ends.  The 
value  of  the  magnetic  force  in  this  field  due  to  the  current  is 


CONTINUITY   OP   THE    MAGNETIC   STATE.  7 

,  where  C  is  the  current  in  absolute  electro-magnetic 
units,*  and  n  is  the  number  of  turns  in  the  winding  per  centi- 
metre of  the  length  of  the  solenoid.  Reducing  this  to  practical 
units,  the  magnetic  force  within  the  solenoid  is  1*257  times  the 
number  of  ampere-turns  per  centimetre  of  the  lengtn. 

Again,  a  nearly  uniform  field  may  be  produced  by  taking  two 
similar  magnets  with  flat  ends  and  placing  them  in  line  with 
their  flat  ends  parallel,  so  that  the  north  pole  of  one  nearly 
touches  the  south  pole  of  the  other.  In  the  narrow  gap 
between  the  ends  facing  one  another  there  is  a  strong  mag- 
netic field,  through  which  the  lines  of  force  pass  almost  straight 
across  from  one  face  to  the  other.  The  field  is  very  nearly 
uniform  except  at  the  edges. 

§  6.  Continuity  of  the  Magnetic  State. — We  have  seen  that 
the  magnetism  of  a  magnetised  bar  may  be  described  by  refer- 
ence to  its  ends,  where  the  imaginary  positive  and  negative 
magnetic  substance  is  accumulated,  the  middle  parts  being  in- 
active. From  another  point  of  view  the  magnetisation  extends 
throughout  the  whole  substance.  We  may  think  of  every  por- 
tion of  the  magnet  as  polarised;  that  is  to  say,  every  particle 
or  elementary  piece  of  the  bar  may  be  regarded  as  a  separate 
magnet.  Throughout  the  middle  portion  of  the  length  these 
elementary  pieces  are  grouped  so  that  each  pole  of  one  touches 
the  opposite  pole  of  its  next  neighbour,  and  the  result  is  that 
the  middle  portion  of  the  bar  shows  no  positive  or  negative 
magnetism ;  but  at  the  ends  the  poles  of  the  elementary  pieces 
are  no  longer  neutralised,  and  the  poles  of  the  pieces  there 
become  the  poles  of  the  bar.  This  is  the  modern  view  of  the 
matter,  and  is  in  many  ways  an  advance  on  the  simple  polar 
view.  It  is  borne  out  by  the  fact,  experimentally  observed, 
that  when  a  magnet  is  cut  up  into  pieces,  however  small,  each 
piece  is  a  separate  magnet. 

§  7.  Intensity  of  Magnetisation. — From  this  point  of  view 
we  are  to  regard  the  magnetic  state  as  existing  continuously 
throughout  the  bar.  If  this  state  is  uniform  from  end  to  end 


*  The  absolute  electro-magnetic  unit  of  current  in  the  C.-G.-S.  system 
is  equal  to  10  amperes. 


8  MAGNETISM  IN  IRON 

of  a  bar,  the  metal  is  said  to  be  uniformly  magnetised.  If  we 
could  cut  up  such  a  bar  by  cross-sections  into  short  lengths  with- 
out disturbing  the  uniformity  of  the  magnetisation,  we  should 
find  every  part  to  be  a  magnet  with  the  same  pole-strength  as 
the  original  bar.  If  we  could  split  it  by  longitudinal  sections  we 
should  find  the  pole-strength  of  each  part  to  be  proportional  to 
the  area  of  cross-section  in  that  part.  In  other  words,  if  we 
could  cut  up  the  bar  in  any  manner  (always  without  altering  the 
magnetic  state  of  the  metal)  we  should  find  that  the  pieces  were 
separate  magnets  of  which  the  moments  were  proportional  to  the 
volumes  of  the  pieces.  The  magnetic  moment  of  each  piece 
will  be  the  same  fraction  of  the  magnetic  moment  of  the  uncut 
bar  as  the  volume  of  the  piece  is  of  the  volume  of  the  uncut 
bar.  The  magnetic  state  which  existed  throughout  the  bar 
before  it  was  cut,  and  exists  throughout  each  piece  after  cutting, 
may  be  specified  if  we  state  the  moment  per  cubic  centimetre  of 
the  metal.  This  quantity  is  called  the  intensity  of  magnetisa- 
tion, and  is  usually  denoted  by  I. 

§  8.  Relation  of  I  to  Pole-Strength. — Let  M  be  the  moment 
of  a  uniformly  magnetised  straight  bar ;  let  I  be  the  length  of 
the  bar  in  centimetres,  s  its  area  of  cross-section  in  square  centi- 
metres, and  m  its  pole-strength. 

Then  M  =  m£ 

The  volume  of  the  bar  is  si;  hence  I,  which  is  M  divided 

by  the  volume,  is  — ,  or  — . 

Si  8 

We  might,  therefore,  have  defined  I  as  the  pole-strength  per 
square  centimetre  of  sectional  area.  It  is  useful  to  remember 
that  I  has  also  this  meaning,  but  the  essential  idea  implied  in 
the  phrase  "  intensity  of  magnetisation  "  is  better  conveyed  by 
the  definition  of  I  given  above.  We  are  to  think  of  I  as  the 
measure  of  a  polarised  state  which  has  a  true  existence  every- 
where in  the  substance  of  the  metal,  though  it  manifests  itself 
only  at  the  ends,  so  far  as  external  action  is  concerned. 

§  9.  Ring  Magnet. — The  usefulness  of  this  idea  will  be  at  once 
apparent  if  we  consider  what  happens  when  a  uniformly  mag- 


LINES    OF   MAGNETISATION,  9 

netised  rod  is  bent  round  into  a  ring  until  the  ends  meet.  There 
are  now  no  poles :  those  that  existed  in  the  rod  have  met  and 
have  neutralised  each  other  ;  there  is  now  no  magnetic  moment, 
and  the  ideas  of  poles  and  moment  will  no  longer  serve  as  means 
of  stating  the  magnetic  state  of  the  ring.  But  the  ring  is  still 
magnetised :  if  we  were  to  cut  it  in  pieces  we  should  find  the 
pieces  to  be  magnets.  The  magnetic  state  expressed  by  the 
quantity  I  still  exists  within  the  metal  :  there  is  a  definite 
"  intensity  of  magnetisation  "  throughout.  If  we  were  to  cut  a 
narrow  gap  through  the  ring  we  should  find  on  one  side  of  the 
gap  a  positive  pole,  and  on  the  other  side  a  negative  pole,  and 
the  strength  of  each  would  be  I  s. 

§  10.  Lines  of  Magnetisation. — Suppose  such  a  gap  or 
crevasse  to  be  cut,  the  number  of  lines  of  force  which  cross 
the  gap  is  4  TT  I  s  (by  §  4),  and  hence  the  magnetic  force 
within  the  gap  (which  is  the  number  of  lines  of  force  per 
square  centimetre)  is  4  TT  \  ;  so  far,  that  is  to  say,  as  the 
magnetic  force  there  is  due  to  the  magnetism  of  the  ring.  Of 
course  there  may  be  additional  magnetic  force  within  the  gap 
due  to  other  magnets  or  to  electric  currents  in  the  neighbour- 
hood ;  but  for  the  present  we  may  confine  our  attention  to  the 
force  that  exists  there  on  account  of  the  magnetisation  of  the 
ring  itself  alone.  The  same  lines  4  TT  I  s  which  cross  the  gap 
may  be  conceived  as  extending  continuously  round  the  ring 
through  the  substance  of  the  metal.  Each  line  forms  a  closed 
curve :  a  short  part  of  it  is  in  the  gap,  the  greater  part  is  in 
the  metal.  We  may  call  the  parts  of  the  lines  which  lie  within 
the  metal  lines  of  magnetisation.  The  name  "  lines  of  force," 
which  is  applicable  to  the  lines  in  the  gap,  is  inappropriate  to 
those  parts  of  the  lines  which  lie  within  the  metal,  because  the 
lines  within  the  metal  do  not  form  a  measure  of  the  magnetic 
force  there. 

§  11.  Lines  of  Magnetisation  (continued). — Fig.  4  illustrates 
the  supposed  case  of  a  narrow  gap  or  crevasse,  A  B,  cut  across  the 
substance  of  a  magnetised  ring  at  any  place  in  its  circumference. 
Within  the  metal  we  have  the  lines  of  magnetisation  which  are 
shown  by  dotted  lines  in  the  figure.  The  number  of  these,  per 
square  centimetre  of  cross-section,  is  4  TT  I.  These  lines  are  con- 


10 


MAGNETISM    IN    IRON. 


tinuous  closed  curves,  and  pass  across  the  gap,  forming  lines  of 
force  there.  If  we  measure  the  magnetic  force  within  the 
crevasse,  we  shall  find  it  equal  to  this  quantity,  4  TT  I,  together 
with  whatever  other  magnetic  force  may  act  there  in  con- 
sequence of  electric  currents  or  magnets  in  the  neighbourhood. 
That  part  of  the  magnetic  force  within  the  crevasse  which  is 
represented  by  4  TT  I,  is  directly  due  to  the  breach  which  we 
have  made  in  the  continuity  of  the  magnetised  ring.  It  may 
be  regarded  as  existing  there  in  consequence  of  the  fact  that 
lines  of  magnetisation  within  the  metal  are  necessarily  con- 
tinuous with  lines  of  force  outside  the  metal. 


Fia.  4. 

Take  another  way  of  looking  at  the  matter.  We  may  think 
of  this  force  within  the  crevasse  A  B  as  due  to  free  magnetism 
on  the  surfaces  A  and  B.  When  we  cut  the  crevasse  in  the 
magnetised  ring,  we  bring  into  existence  a  positive  pole  which 
is  distributed  over  the  surface  at  A,  and  a  negative  pole  which 
is  distributed  over  the  surface  at  B.  The  strength  of  each  of 
these  poles  is  I  s,  and  the  surface-density  of  free  magnetism — 
that  is  to  say,  the  amount  of  free  magnetism  per  square  centi- 
metre of  surface — is  I.  By  a  well-known  proposition  in  the 


MAGNETIC   FORCE    WITHIN    THE    METAL.  11 

theory  of  attraction,  a  plate  on  which  the  surface-density  is  I 
attracts  a  unit  particle  placed  close  to  it  with  a  force  equal  to 
2  TT  I  (except  near  the  edge,  where  the  force  is  less).  Let  a  unit 
positive  magnetic  pole,  then,  be  placed  in  the  crevasse.  The 
plate  of  free  magnetism  on  A  repels  it  with  the  force  2  TT  I  ;  the 
plate  of  free  magnetism  on  B  attracts  it  with  an  equal  force. 
The  whole  force  at  a  point  in  the  crevasse,  due  to  the  magnet- 
isation of  the  ring,  is  the  joint  force  exerted  by  the  two  plates; 
in  other  words,  it  is  4  TT  I. 

Suppose  now  that  the  uniformly  magnetised  magnetic  ring  is 
stretched  out  to  form  a  straight  bar.  If  we  imagine  a  crevasse 
to  be  cut  across  it  at  any  part  of  its  length,  we  shall  still  find 
in  the  crevasse  the  lines  4  TT  \  per  square  centimetre  due  to 
the  continuous  magnetisation  of  the  bar,  in  addition  to  what- 
ever lines  of  force  may  exist  there  in  consequence  of  electric 
circuits  or  free  magnetism  in  the  neighbourhood  (excluding,  of 
course,  the  free  magnetism  on  the  faces  of  the  crevasse,  to 
which  the  lines  4  TT  I  are  directly  due).  The  whole  field  within  the 
imaginary  crevasse  may  therefore  be  thought  of  as  made  up 
of  two  components,  namely,  (1)  the  lines  of  magnetisation,  the 
number  of  which  is  4  ir  \  per  square  centimetre ;  and  (2)  the 
magnetic  force  due  to  external  causes,  namely,  that  which 
is  due  to  electric  currents  and  free  magnetism  in  the  neigh- 
bourhood. Amongst  the  causes  of  this  magnetic  force  is  to 
be  included  the  free  magnetism  at  the  ends  of  the  bar  itself,  as 
well  as  the  poles  of  any  other  magnets  which  may  be  near 
enough  to  produce  any  sensible  effect. 

§  12.  Magnetic  Force  within  the  Metal. — The  magnetic 
force  due  to  external  causes — that  is,  to  magnets  or  electric  cur- 
rents in  the  neighbourhood — which  has  just  been  described  as 
constituting  one  part  of  the  magnetic  force  which  we  should 
measure  in  a  crevasse,  is  to  be  thought  of  as  acting  also 
within  the  uncut  substance  of  the  metal  itself.  It  consti- 
tutes the  whole  magnetic  force  there.  We  shall  denote  the 
magnetic  force  by  H.  It  must  be  borne  in  mind  that  in 
reckoning  the  value  of  H  at  any  point  within  the  substance 
of  a  piece  of  magnetised  metal,  account  is  to  be  taken  not 
merely  of  the  forces  due  to  electric  currents  and  to  ter- 
restrial magnetism  and  to  the  poles  of  other  magnets,  but 


12  MAGNETISM   IN   IRON. 

also  of  the  forces  which  are  contributed  by  the  poles  of  the 
piece  itself. 

§  13.  Magnetic  Induction. — The  whole  group  of  lines  which 
cross  the  crevasse  is  to  be  conceived  as  existing  within  the  metal 
before  the  crevasse  was  cut,  partly  as  lines  of  magnetisation  and 
partly  as  lines  of  force.  The  whole  group  of  lines  which  cross 
the  imaginary  crevasse  consists  (per  square  centimetre)  of  the 
resultant  of  4  TT  I  and  H.  This  resultant  is  called  the  magnetic 
induction  within  the  metal,  and  is  denoted  by  B.  The  quan- 
tities 4  TT  I  and  B  are  vectors,  having  direction  as  well  as  mag- 
nitude, and  are  to  be  compounded  as  forces  or  velocities  are 
compounded.  If  H  and  I  happen  to  have  the  same  direction, 
B  is  numerically  equal  to  the  sum  of  4  TT  I  and  H.  In  any  case 

the  equation  B  =  4  TT  I  +  H 

is  true  when  understood  in  the  vector  sense,  that  B  is  the 
resultant  of  4  TT  I  and  H.  In  most  of  the  cases  that  are  of  prac- 
tical interest  H  has  either  the  same  direction  as  B  or  it  has 
the  opposite  direction,  so  that  the  above  equation  holds  good 
in  the  numerical  sense  when  the  proper  sign  (  +  or  -  )  is  given 
to  H,  according  as  it  assists  or  opposes  the  magnetisation. 

§  14.  Distinction  between  Magnetic  Induction  and  Mag- 
netic Force  within  the  Metal. — The  lines  of  magnetic  induc- 
tion (B)  within  the  bar  are  continuous  with  the  lines  of 
magnetic  force  in  the  space  outside — that  is  to  say,  every 
Line  of  Force  outside  is  completed,  so  that  it  forms  a  closed 
curve,  by  a  Line  of  Induction  inside.  For  many  purposes 
B  is  the  most  important  quantity  by  which  the  magnetisation 
of  a  magnet  may  be  specified.  In  a  dynamo,  for  instance,  it  is 
the  value  of  B  in  the  armature  core  that  determines  the 
strength  of  the  magnetic  circuit.  The  analysis  of  B  into  two 
components,  H  and  47r|,  is  no  doubt  highly  artificial,  but 
it  is  of  service  when  we  have  to  deal  with  the  relations  which 
exist  between  the  magnetism  of  a  magnet  and  the  influences 
which  are  affecting  its  magnetism  from  outside.  The  student 
will  find  it  useful  to  picture  to  himself  the  state  of  a  magnet  at 
any  point  of  its  substance  by  thinking  of  two  groups  of  lines  as 
passing  through  the  metal,  namely,  4  TT  |  and  H,  which  combine 


PARTICULAR   CASES.  13 

to  form  a  resultant  group  B.  To  obtain  B  directly  we  have 
only  to  imagine  a  narrow  crevasse  cut  across  the  magnet :  B  is 
measured  by  the  force  a  unit  pole  would  experience  if  placed 
in  such  a  crevasse ;  in  other  words,  it  is  the  number  of  lines 
which  cross  the  crevasse  per  square  centimetre  of  cross-section. 
If,  on  the  other  hand,  we  wish  to  isolate  the  magnetic  force  H 
that  acts  at  any  point  within  the  metal,  we  may  imagine  a 
hole  drilled  through  the  magnet  from  end  to  end  in  the  direc- 
tion of  magnetisation,  and  passing  through  the  point  at  which 
H  is  to  be  measured.  The  force  which  a  unit  pole  would  expe- 
rience if  placed  in  the  hole  at  that  point  is  H.  That  this  is  so 
will  be  evident  when  it  fa  remembered  that  there  is  no  free 
magnetism  on  the  sides  of  the  hole,  because  it  is  supposed  to  be 
drilled  in  the  direction  of  magnetisation,  and  the  force  within 
it  is,  therefore,  due  solely  to  the  outside  influences  which  give 
rise  to  the  magnetic  force  H,  as  denned  in  §  12,  namely,  the 
free  magnetism  at  the  ends  of  the  magnet  and  any  other 
magnets  or  currents  that  are  near. 

It  is  only  at  points  inside  the  metal  that  we  need  distinguish 
the  magnetic  force  H  from  the  magnetic  induction  B.  Outside, 
at  points  in  non-magnetisable  space,  the  magnetic  induction  is 
identical  with  the  magnetic  force.  There  is  no  discontinuity  in 
the  lines  of  ind uction  where  they  pass  into  the  metal  or  out 
of  it. 

§  15.  Particular  Oases. — The  following  illustrations  may  help 
to  make  these  definitions  intelligible.  Take  a  ring  electro-magnet 
consisting  of  an  iron  core,  wound  with  a  solenoid  of  n  turns  per 
centimetre,  and  let  a  current,  C,  flow  in  the  solenoid.  The  mag- 
netic force  within  the  solenoid,  due  to  this  current,  is  approxi- 
mately equal  to  4  TT  C  n  at  all  points.  If  there  are  no  neighbour- 
ing magnets  or  other  sources  of  magnetic  force,  this  is  the  value 
of  H  which  acts  on  the  metal  of  the  ring.  Next,  let  the  ring 
be  cut  and  straightened  into  a  bar,  with  the  solenoid  still  ov 
it,  through  which  the  current  C  flows.  The  magnetic  force  du& 
to  the  current  is  still  sensibly  equal  to  4  TT  C  ft  (except  near  the 
ends).  But  we  now  have  another  term  to  consider  in  reckoning 
H.  The  free  magnetism  residing  at  the  ends  of  the  bar  pro- 
duces magnetic  force  at  all  points  in  the  interior,  as  well  as 
at  points  in  the  space  outside,  and  H  is  the  resultant  of 


14  MAGNETISM    IN    IRON. 

this  force,  together  with  the  force  47rCn  due  to  the  cur 
rent.  The  force  due  to  the  free  magnetism  at  the  ends  is 
opposite  in  direction  to  that  due  to  the  current  j  hence  H  at 
any  point  within  the  metal  is  less  than  4  TT  C  n  by  an  amount 
which  depends  on  the  distance  of  the  point  considered  from  the 
ends  of  the  bar.  The  longer  the  bar  is  the  more  nearly  will  H 
be  identical  with  4  TT  C  T&,  and  if  the  bar  is  very  long,  so  that 
the  ends  are  too  far  removed  to  have  any  material  influence,  we 
may  take  the  magnetic  force  on  central  portions  as  sensibly 
equal  to  4  TT  C  n. 

Again,  in  a  permanent  bar-magnet  there  is  at  any  point  a 
certain  magnetic  force,  H,  due  to  the  free  magnetism  at  the 
ends,  and  opposite  in  direction  to  the  lines  of  magnetisation 
within  the  metal.  We  may  call  this  the  self-demagnetising 
force  exerted  by  the  bar,  since  its  tendency  is  to  reduce  the  bar's 
magnetisation. 

Again,  a  long  piece  of  straight  iron  wire  stretched  in  the 
direction  of  the  lines  of  force  of  the  earth's  magnetic  field  is 
acted  on  by  a  magnetic  force,  H,  equal  to  the  force  of  the  earth's 
field.  If  the  wire  is  hung  vertically  it  is  convenient  to  treat 
the  earth's  field  as  consisting  of  a  horizontal  and  a  vertical  com- 
ponent. The  former  is  a  magnetic  force  which  acts  across  the 
wire ;  the  latter  is  in  this  case  much  the  more  important  of  the 
two,  for  it  constitutes  the  whole  longitudinal  part  of  the  mag- 
netic force  H,  and,  as  we  shall  presently  see,  it  is  upon  this 
almost  wholly  that  the  magnetisation  of  the  wire  depends. 

§  16.  Magnetic  Permeability. — In  general,  when  a  substance 
is  placed  in  a  magnetic  field  it  becomes  magnetised.  The 
connection  between  the  magnetism  it  acquires  and  the  mag- 
netic force  which  acts  upon  it  may  be  expressed  in  two  ways. 

One  of  these  ways  is  to  compare  the  magnetic  induction  B 
which  is  produced  in  the  metal  with  the  magnetic  force  H  to 
which  that  induction  is  due.  For  many  purposes  this  is  the 
most  convenient  way. 

To  fix  our  ideas  let*  us  think  of  a  very  long  uniform  rod  placed 
in  a  uniform  field  of  magnetic  force,  with  the  direction  of  its 
length  parallel  to  that  of  the  lines  of  force.  When  the  rod 
becomes  magnetised  its  ends  disturb  the  field  of  force,  but  we 
can  get  rid  of  any  trouble  about  the  ends  by  thinking  of  thti 


MAGNETIC    PERMEABILITY.  15 

rod  as  indefinitely  long,  or  so  long  that  the  influence  which  the 
ends  have  on  the  value  of  the  magnetic  force  is  negligible. 
Let  the  uniform  magnetic  field  exert  a  certain  force,  H,  on  the 
rod.  This  produces  within  the  rod  a  certain  induction,  B,  the 
value  of  which  might  be  measured  by  cutting  a  narrow  crevasse 
acroos  the  rod  at  any  place,  and  measuring  the  number  of  lines 
per  square  centimetre  which  cross  the  crevasse. 

If  the  rod  is  of  iron,  nickel,  or  cobalt,  it  will  be  found  that 
the  number  of  lines  of  induction  B  per  square  centimetre 
within  the  rod  is  much  greater  than  the  number  of  lines  per 
square  centimetre  in  the  field.  This  fact  may  be  expressed  by 
saying  that  the  material  of  the  rod  is  more  permeable  with 
respect  to  lines  of  magnetic  induction  than  is  the  space  or 
medium  surrounding  it.  In  Faraday's  expressive  language, 
the  material  of  rod  has  greater  conductivity  for  the  lines  of 
induction  than  the  surrounding  space  or  medium  has.  We 
may  think  of  the  lines  as  crowding  by  preference  into  the  rod, 
finding  an  easier  path  through  it  than  through  the  surrounding 
medium. 

The  quality  in  virtue  of  which  the  material  of  the  rod  con- 
ducts the  lines  better  than  empty  space  conducts  them,  is  called 
Its  magnetic  permeability.  This  phrase  was  introduced  by 
Lord  Kelvin  in  his  mathematical  development  of  the  subject, 
as  a  synonym  for  Faraday's  "  Conducting  power  of  a  magnetic 
medium  for  lines  of  force." 

In  the  case  we  have  supposed,  of  an  indefinitely  long  rod,  the 
magnetic  force  at  any  point  within  the  metal  has  the  same  value 
as  the  magnetic  force  at  any  neighbouring  point  in  the  space 
outside,  since  the  force  is  not  disturbed  by  the  magnetisation 
of  the  rod.  In  such  a  case  we  might  define  the  permeability  as 
the  number  (per  square  centimetre)  of  lines  of  induction  B 
in  the  rod  to  the  number  (per  square  centimetre)  of  lines 
of  force  in  the  space  outside.  But  if  we  wish  a  definition 
which  will  be  of  more  general  application — applying  to  short 
rods  as  well  as  to  long  ones,  and  to  other  forms  of  magnet — we 
have  to  bear  in  mind  that  the  surrounding  field  is  generally 
disturbed  by  the  magnetisation  of  the  piece.  What  has  to  bo 
compared  is  the  induction  at  any  place  in  the  metal  with  tha 
magnetic  force  which  is  in  operation  there ;  in  other  words, 
we  may  define  the  permeability  as  the  ratio  of  the  induction 


16  MAGNETISM   IN    IRON. 

B  at  any  point  of  the  metal  to  the  magnetic  force  H  which 
acts  within  the  metal  at  that  point.  The  permeability  is 
usually  denoted  by  ft  ;  so  that  we  have 


In  this  definition  it  is  to  be  understood  that  B,  the  magnetic 
induction,  has  been  produced  by  subjecting  the  material  to  a 
magnetic  force,  H. 

§  17.  Permeability  of  Paramagnetic  and  Diamagnetic  Sub- 
stances. —  A  paramagnetic  substance  is  one  in  which  the  per- 
meability is  greater  than  that  of  empty  space.  In  other  words, 
when  such  a  substance  is  placed  in  a  magnetic  field  it  will 
become  magnetised  in  such  a  way  that  B  is  greater  than  H. 
The  lines  of  force  of  the  surrounding  field  will  converge  more  or 
less  towards  it,  preferring  it  to  the  neighbouring  space  as  a 
magnetic  "conductor."  Iron,  nickel,  and  cobalt  are  para- 
magnets  with  exceedingly  great  permeability. 

In  a  diamagnetic  substance,  on  the  other  hand,  the  per- 
meability is  less  than  that  of  empty  space.  When  such  a 
substance  is  placed  in  a  magnetic  field,  the  lines  of  force  more 
or  less  avoid  it  as  a  bad  "conductor,"  preferring  the  space 
outside.  No  substance  is  more  than  slightly  diamagnetic. 
Even  in  bismuth,  which  is  the  most  highly  diamagnetic 
substance  known,  the  magnetic  permeability  is  very  little  less 
than  unity  :  its  value  is  about  0'999S2. 

The  permeability  of  air  is  sensibly  the  same  as  that  of  empty 
space.  Hence,  when  a  magnetic  field  is  formed  in  air,  the  lines 
cf  induction  are  indistinguishable  from  the  lines  of  force.  It  is 
only  when  the  lines  pass  into  a  substance  which  is  either  para- 
magnetic or  diamagnetic  that  the  distinction  between  magnetic 
force  and  magnetic  induction  must  be  maintained. 

§  18.  Illustrations  of  Permeability.  —  By  way  of  illustrating 
the  behaviour  of  paramagnetic  and  diamagnetic  substances 
when  placed  in  a  magnetic  field,  Fig.  5  and  Fig.  6  have 
been  copied  from  one  of  Lord  Kelvin's  Papers.*  In  Fig.  5  a 
magnetic  field  which  was  originally  uniform  has  been  disturbed 

*  Reprint  of  Paper  on  "  Electrostatics  and  Magnetism,"  pp.  489  and  491. 


ILLUSTRATIONS    OP   PERMEABILITY. 


17 


by  having  a  sphere  of  exceedingly  permeable  material  placed 
in  it.  Before  the  sphere  was  placed  in  the  field  the  lines  of 
force  were  straight,  parallel,  and  equally  spaced.  The  effect  of 
introducing  the  sphere  is  to  make  them  converge  upon  it  in  the 


FIG.  5. — Disturbance  of  an  originally  uniform  magnetic  field  by  the  intro 
duction  of  a  soft  iron  sphere. 


FIG.  6. — Disturbance  of  an  originally  uniform  magnetic  field  by  the  intro- 
duction of  a  sphere  of  strongly  diamagnetic  material. 


manner  which  has  been  exactly  represented  in  the  figure  from 
which  Fig.  5  is  copied.  Outside  the  sphere  the  lines  may  be 
called  indifferently  lines  of  induction  or  lines  of  force  (§  14). 
The  lines  inside,  which  have  been  added  in  this  copy,  are 
continuous  with  them,  and  are  lines  of  induction.  The  mag- 

C 


18  MAGNETISM   IN    IRON. 

netic  induction  within  the  sphere  is  uniform.  Fig.  5  may  be 
taken  to  represent  what  happens  when  a  homogeneous  spherical 
ball  of  soft  iron  is  placed  in  an  originally  uniform  magnetic 
field. 

Fig.  6  shows  in  the  same  way  how  an  originally  uniform  field 
of  force  is  disturbed  by  the  introduction  of  a  sphere  of  diamag- 
netic  material.  The  material  here  is  a  purely  imaginary  one, 
with  permeability  barely  one-half  that  of  the  surrounding 
medium,  and  is  far  more  highly  diamagnetic  than  any  actual 
substance. 

The  student  will  not  fail  to  notice  that  the  convergence  or 
divergence  of  the  lines  of  induction,  illustrated  by  these  typical 
cases,  depends  on  whether  the  permeability  of  the  body  is 
greater  or  is  less  than  the  permeability  of  the  medium  in 
which  it  is  placed.  If  the  surrounding  medium  were  itself 
a  paramagnetic  substance,  the  case  shown  in  Fig.  6  might  be 
realised  by  choosing  for  the  material  of  the  spherical  ball  a 
substance  whose  permeability  was  about  half  (more  exactly 
0'48  times)  that  of  the  substance  surrounding  it. 

We  shall  return  to  these  figures  later,  in  speaking  of  the 
influence  which  the  form  of  the  body  that  is  placed  in  a 
magnetic  field  exercises  on  the  amount  of  magnetic  induction 
within  the  body. 

§  19.  Magnetic  Susceptibility. — When  a  substance  is  mag- 
netised by  subjecting  it  to  the  action  of  magnetic  force,  the 
relation  of  the  induction  B  to  the  force  H  measures,  as  we 
have  seen,  the  permeability  of  the  substance.  But  instead  of 
expressing  the  magnetisability  of  the  substance  by  stating  the 
relation  of  the  induction  B  to  the  force  H,  we  may  state  it  in 
a  different  way  by  giving  the  relation  of  the  intensity  of  mag- 
netisation I  to  the  force  H.  The  ratio  of  the  intensity  of 
magnetisation  to  the  magnetic  force  producing  it  is  called  the 
magnetic  susceptibility  of  the  substance,  and  is  usually  denoted 
by  K  ;  thus  . 

K=F 

§  20.  Connection  of  the  Ideas  of  Permeability  and  Sus- 
ceptibility.—We  have  seen  (§  13)  that 


CONNECTION   OF   IDEAS   OP   PERMEABILITY,    ETC.  19 

and  by  definition  of  the  susceptibity  K,  I  =  K  H  J 
Hence  B  =  4?rK 


But  by  definition  of  the  permeability  ju,  B  =  /*  H  ; 
Hence  /A 


and  K  = 


4:TT 


In  a  substance  such  as  air,  in  which  the  permeability  Is  unity, 
the  magnetic  susceptibility  is  zero.  In  a  paramagnetic  sub* 
stance,  in  which  p,  is  greater  than  1,  the  susceptibility  is  positive. 
In  a  diamagnetic  substance,  in  which  the  permeability  is  less 
than  1,  the  susceptibility  is  negative. 

In  other  words,  a  paramagnetic  substance  when  subjected  to 
magnetic  force  acquires  a  magnetisation  I,  which  is  in  the  same 
direction  as  the  force,  and  so  makes  B  greater  than  H.  A  dia- 
magnetic, on  the  other  hand,  acquires  a  magnetisation  I,  which 
is  opposite  to  the  force,  and  so  makes  B  less  than  H. 

§  21.  A  word  of  caution  is,  perhaps,  desirable  here  as  to  the 
application  of  the  equations  which  have  just  been  given.  It 
has  been  assumed  that  the  material  to  which  the  magnetic  force 
H  has  been  applied,  has  no  magnetism  except  what  the  force 
itself  induces.  If  other  forces  had  acted  before,  leaving  residual 

D 

magnetisation,    the  ratio  —  would  not  be  a  true  measure  of 

H 

the  permeability,  nor  would  the  ratio  —  .  be  a  true  measure  of 

H 
the  susceptibility. 

Again,  it  has  been  assumed  that  the  material  is  magnetically 
isotropic  —  that  is  to  say,  that  a  lump  of  it  is  equally  capable 
of  taking  magnetisation  in  all  directions.  If  this  were  not  so, 
if  the  magnetic  properties  of  the  substance  were  different  in 
different  directions  (as  would,  for  instance,  be  the  case  to  some 
extent  in  a  piece  of  iron  cut  from  a  rolled  plate),  it  would 
be  necessary,  if  we  wished  to  specify  fully  the  relation  of 
the  magnetisation  to  the  magnetic  force,  to  resolve  the  force 

c2 


20  MAGNETISM    IN    IRON. 

into  components  along  axes  chosen  in  the  directions  which 
give  greatest  susceptibility  and  least  susceptibility,  find  the 
component  magnetisation  in  each  of  those  directions  by 
multiplying  each  component  force  by  the  value  which  the 
susceptibility  has  in  that  direction,  and  then  compound  these 
components  of  magnetisation  to  find  the  resultant  value  of  I. 
In  such  a  case  the  direction  of  the  resultant  magnetisation  will 
not  in  general  coincide  with  that  of  the  resultant  magnetic 
force,  and  the  equation  B  —  4  TT  |  +  H  will  be  true  only  when 
interpreted  in  its  vector  sense. 

But  in  the  cases  of  magnetisation  in  iron  which  have  ordi- 
narily to  be  dealt  with,  it  is  not  necessary  to  take  account  of 
this  consideration,  for  the  material  is  either  sufficiently  nearly 
isotropic,  or  the  direction  of  the  applied  magnetic  force  coin- 
cides with  an  axis  of  greatest  or  least  magnetic  susceptibility, 
and  the  effect  is  that  I  and  B  have  the  same  direction  as  H. 

§  22.  Influence  of  the  Form  of  Bodies  on  the  Magnetisation 
induced  in  them. — When  a  body  is  placed  in  a  magnetic  field 
the  degree  to  which  it  becomes  magnetised  depends  not  only 
on  the  original  strength  of  the  field  and  on  the  permeability  of 
the  substance,  it  depends  also  (often  in  very  great  measure)  on 
the  form  of  the  body.  This  is  because  the  body,  in  becoming 
magnetised,  generally  disturbs  the  field,  causing  the  magnetic 
force  at  any  point  within  or  near  the  body  to  be  different  from 
the  force  that  existed  there  before  the  body  was  introduced. 
The  free  magnetism  which  is  developed  by  the  body's  magneti- 
sation contributes  to  produce  magnetic  force,  and  so  affects  the 
resultant  value  of  the  force  at  any  point,  inside  the  body  or 
outside,  that  is  not  too  far  off'  to  be  sensibly  affected.  With 
iron  and  other  very  susceptible  materials  this  disturbance  of 
the  field  is  often  so  great  that  the  original  value  of  the  mag- 
netic force  is  not  even  a  rough  approximation  to  the  value 
the  force  assumes  when  modified  by  the  magnetisation  of  the 
body.  The  intensity  of  magnetisation  at  any  point  within  the 
body  depends  on  the  actual  value  which  the  magnetic  force 
assumes  at  that  point,  and  this  in  its  turn  depends  partly 
upon  the  magnetisation  of  the  body  as  a  whole.  When 
we  wish  to  examine  the  magnetic  susceptibility  or  per- 
meability of  a  substance,  we  require  to  know  the  actual  value 


INFLUENCE    OF    FORM    ON    MAGNETISATION.  21 

of  the  magnetic  force  within  it,  for  the  purpose  of  comparing 
that  with  the  intensity  of  magnetisation,  or  with  the  magnetic 
induction  there.  The  permeability  is  measured  by  the  propor- 
tion which  the  induction  B  bears  to  the  strength  which  the 
magnetic  force  H  actually  has  at  the  same  place,  not  to  the 
strength  which  it  may  have  had  there  before  the  body  was  in- 
troduced, nor  to  the  strength  which  it  may  still  have  in  external 
parts  of  the  field. 

We  have,  therefore,  to  take  account  of  what  may  be  called 
the  reaction  of  the  magnetised  body  upon  the  magnetising 
field. 

In  very  many  cases  the  reaction  of  the  body  upon  the  field  is 
too  complex  to  allow  a  mathematical  examination  of  it  to  be 
practicable.  With  bodies  of  irregular  form  it  is  out  of  the 
question  to  calculate  beforehand  what  will  be  the  magnetic 
force  and  the  magnetic  induction  at  internal  points,  having 
given  the  original  strength  of  the  external  field  and  the  per- 
meability of  the  substance.  The  problem  is  determinate,  but  too 
difficult  to  attack.  Even  so  apparently  simple  a  case  as  that  of 
a  short  cylindrical  iron  rod  with  flat  ends,  placed  lengthwise  in 
an  originally  uniform  field,  presents  difficulties  so  formidable 
that  no  exact  solution  has  been  given.  The  difficulty  in  the 
case  of  such  a  rod  is  aggravated  by  the  fact  that  even  though 
the  rod  be  perfectly  homogeneous  to  begin  with,  the  suscepti- 
bility or  the  permeability  is  not  uniform  throughout  when  the 
rod  becomes  magnetised.  This  is  because  the  magnetisation  is 
not  uniform,  and,  as  we  shall  see  later,  the  permeability  of  iron 
depends  to  a  considerable  extent  on  the  intensity  of  magnetisa- 
tion. The  reaction  of  the  rod  upon  the  original  field  tends  to 
reduce  the  magnetic  force  at  internal  points,  but  this  effect  is 
unequal  at  different  parts  of  the  length.  It  is  least  at  the 
middle  of  the  length;  hence  the  magnetic  force,  and  conse- 
quently the  induction  also,  is  greatest  there  and  is  less  near 
the  ends. 

§  23.  Long  Rod  placed  Lengthwise  in  a  Uniform  Field. — 

When  the  rod  is  long  in  comparison  with  its  breadth  and  thick- 
ness the  effect  of  its  free  magnetism  in  reducing  the  magnetic 
force  is  less  than  when  the  rod  is  short,  especially  in  the  middle 
region  of  the  length,  because  the  ends,  in  which  the  free  mag« 


22  MAGNETISM  IN  moN. 

netism  chiefly  resides,  are  too  far  off  to  have  much  influence. 
The  amount  of  magnetic  induction  is  consequently  greater  in  a 
long  rod  than  in  a  short  one  of  the  same  breadth  and  thickness, 
the  original  strength  of  the  field  and  the  permeability  of  the 
substance  being  the  same  in  both  cases.  When  a  very  long 
rod  is  placed  lengthwise  in  a  uniform  field  the  influence  of  the 
ends  becomes  almost  insensible,  and  the  actual  magnetic  force 
at  points  within  the  rod  is  then  almost  the  same  as  at  points 
outside,  except  near  the  ends.  The  magnetisation  will  be 
practically  uniform  throughout  the  middle  region,  but  will  fall 
off  towards  the  ends. 

When  the  substance  of  the  rod  is  very  permeable,  the  rod 
must  be  very  long  relatively  to  its  transverse  dimensions  before 
we  may  neglect  its  reaction  upon  the  magnetic  field,  and  before 
we  may  treat  the  magnetic  force  at  internal  points  near  the 
middle  as  sensibly  equal  to  the  force  at  external  points,  and 
the  magnetisation  as  nearly  uniform.  When  the  substance 
is  less  permeable  a  shorter  length  will  give  an  equally  good 
approach  to  uniform  force  and  uniform  magnetisation. 

§  24.  Analogy  of  Induced  Magnetisation  to  Electric  Con- 
duction.— The  concentration  of  magnetic  induction  which  takes 
place  when  a  permeable  body  is  placed  in  a  magnetic  field  is 
analogous  to  the  concentration  of  electric  flow  which  may  be 
brought  about  by  immersing  a  piece  of  copper  in  a  tube  full 
of  mercury,  through  which  an  electric  current  is  passing.  Let 
the  tube  be  wide  and  long,  and  let  the  current  in  it  be  uni- 
formly distributed  over  the  whole  cross-section :  we  have  in 
this  the  analogue  of  a  uniform  magnetic  field.  Suppose  a 
short  piece  of  copper  wire  to  be  inserted  and  held  lengthwise 
anywhere  near  the  axis  of  the  tube.  The  lines  of  electric  flow, 
which  before  were  straight  and  parallel,  converge  more  or  less 
towards  the  piece  of  copper,  preferring  to  crowd  into  it  because 
its  conductivity  is  much  greater  than  that  of  the  surround- 
ing medium.  The  whole  current  is  divided  between  the  copper 
and  the  mercury  around  it,  the  copper  taking  a  share  that  is 
greater  than  the  proportion  which  its  cross-section  bears  to  that 
of  the  whole  conducting  tube.  The  current  enters  and  leaves  the 
copper  not  at  the  ends  merely,  but  also  along  the  sides,  especially 
near  the  ends.  If  the  piece  of  copper  is  short,  there  can  be  no 


ANALOGY    OP   MAGNETISATION   TO   CONDUCTION.  23 

more  than  a  slight  convergence  of  the  flow  into  it.  For 
instance,  to  take  an  extreme  case,  a  little  disc  of  thin  copper 
plate  placed  in  the  mercury,  so  that  it  faces  in  the  direction  of 
the  flow,  has  little  more  conduction  through  it  than  through  an 
equal  area  of  the  surrounding  liquid.  In  other  words,  the  disc 
produces  but  a  slight  disturbance  of  the  distribution  of  flow 
in  the  tube.  On  the  other  hand,  a  long  thin  copper  wire  set 
lengthwise  will  gather  much  of  the  flow  into  itself,  and  if  the 
wire  be  very  long  its  share  of  the  whole  will  be  greater  than 
the  amount  taken  by  an  equal  section  of  the  mercury  in  the 
proportion  in  which  the  conductivity  of  copper  is  greater  than 
that  of  mercury.  Substitute  magnetic  permeability  for  electric 
conductivity,  and  magnetic  induction  for  electric  flow,  and  we 
have  a  nearly  perfect  analogue  of  what  happens  when  an  iron 
rod  or  wire  is  placed  in  a  magnetic  field. 

There  is,  however,  this  important  difference,  which  makes 
the  magnetic  case  less  simple  than  the  other.  The  electric 
conductivity  of  the  copper  is  a  constant  quantity,  independent 
of  the  strength  of  current  in  the  metal;  whereas  the  permea- 
bility of  iron  depends  on  the  actual  intensity  of  magnetisation, 
and  consequently  varies  (in  general)  to  some  extent  throughout 
the  piece. 

§  25.  Cases  in  which  the  Magnetisation  is  Uniform : 
Ellipsoid. — In  certain  special  cases  it  happens  that  when  a 
magnetisable  body  is  placed  in  a  uniform  magnetic  field,  the 
magnetic  force  at  all  points  inside  the  body  is  uniform,  though 
its  value  there  is  not  the  same  as  at  external  points.  A  very 
important  instance  in  which  this  is  true  occurs  when  the  form 
of  the  body  is  that  of  an  ellipsoid,  the  material  being  homo- 
geneous, so  that  the  permeability  has  the  same  value  through- 
out. In  such  a  case  it  may  be  shown  that  the  effect  of  an 
originally  uniform  external  field  is  to  produce  a  strictly  uniform 
magnetisation.* 

Let  the  ellipsoidal  body  be  made  of  a  paramagnetic  material, 
such  as  iron,  and  let  it  be  placed  in  a  uniform  field :  then  the 
originally  straight  and  parallel  lines  of  the  field  become  bent, 
so  that  they  converge  on  it,  as  the  lines  converge  on  the  sphere 

*  See  Maxwell's  "  Electricity,"  Vol.  II.,  §§  437-43a 


24  MAGNETISM    IN    IRON. 

in  Fig  5.  The  reaction  of  the  body  on  the  field  is  such  that 
the  magnetic  force  at  outside  points  near  the  body  is  no 
longer  uniform.  But  at  internal  points  the  effect  of  the 
reaction  is  different.  The  force  becomes  uniform  there,  with  a 
value,  however,  which  is  less  than  the  value  it  had  in  the  undis- 
turbed field.  This  uniform  internal  force  implies  uniform  induc- 
tion and  uniform  intensity  of  magnetisation — that  is  to  say, 
each  of  the  quantities  H  and  I  and  B  is  uniform  throughout 
the  whole  of  the  body  ;  but  it  must  be  borne  in  mind  that  H 
differs,  and  often  differs  greatly,  from  the  value  which  the  force 
had  originally,  and  still  has  in  distant  parts  of  the  field.  The 
amount  of  this  difference  will  depend  on  the  shortness  of  the 
ellipsoid  and  the  intensity  of  its  magnetisation.  For  brevity 
we  shall  use  H'  to  designate  what  may  be  called  the  external 
force — that  is,  the  original  value  which  the  force  had  before 
the  field  was  disturbed,  or,  what  is  the  same  thing,  the  value 
which  the  force  still  has  at  distant  external  points;  and  we 
shall  keep  H  to  mean,  as  usual,  the  actual  magnetic  force  at 
points  within  the  metal. 

§  26.  Magnetisation  of  an  Ellipsoid  (continued). — The  case  of 
an  ellipsoid  subjected  to  the  action  of  an  originally  uniform  field 
is  of  so  much  practical  interest  that  it  is  worth  while  to  state  here 
some  of  the  results  of  calculation  which  are  applicable  to  it. 

Suppose  the  ellipsoid  to  be  set  with  one  of  its  axes  pointing 
in  the  direction  of  the  magnetic  force.  Let  c  be  half  the 
length  of  this  axis,  and  a  and  b  half  the  lengths  of  the  other 
axes,  which  point  in  directions  that  are  perpendicular  to  the 
direction  of  the  force.  It  will  suffice  to  take  the  case  of  an 
ellipsoid  of  revolution,  in  which  a  =  b 

The  original  external  force  being  H'  and  the  force  actually 
operative  being  H,  we  have 

where  JN  is  a  number  depending  on  the  relation  of  the 
length  of  the  ellipsoid  to  its  transverse  dimensions.  We  may 
express  JV  in  terms  of  the  eccentricity  e.  When  the  ellipsoid 
is  of  the  prolate  or  elongated  form,  Fig.  7  (the  polar  diameter 
2  c  or  C  C'  greater  than  the  equatorial  diameter  2  a  or  A  A'), 

/  2~ 

-</F? 


MAGNETISATION    OF    AN    ELLIPSOID. 


25 


and 


(1) 


When  the  ellipsoid  is  much  elongated  this  expression  approxi- 
mates to  the  following  simpler  form  :  — 

....    (2) 

When  the  ellipsoid  is  of  the  oblate  or  flattened  form,  Fig.  8 
(the  polar  diameter  2  c  less  than  the  equatorial  diameter  2  a), 


the  eccentricity 


-  - .  and 


(3) 


Fia.  7. 


FIG.  8. 


§  27.  Distribution  of  Free  Magnetism  in  the  Uniformly 
Magnetised  Ellipsoid. — Within  the  ellipsoid  the  lines  of  force 
H,  of  magnetisation  I,  and  of  magnetic  induction  B,  lie,  as  in 
Figs.  7  and  8,  straight  and  parallel  to  the  lines  in  the  undis- 
turbed field.  Since  the  magnetisation  is  uniform  the  free 
magnetism  resides  wholly  on  the  surface.  To  sec  how  it  is  dis- 
tributed over  the  surface  we  have  to  remember  that  I  is  the 
surface  density  of  free  magnetism  per  square  centimetre  on 
every  part  of  an  imaginary  surface  formed  by  taking  an  end 
elevation  of  the  ellipsoid — that  is  to  say,  by  projecting  it 


26 


MAGNETISM   IN    IRON. 


upon  a  plane  which  is  perpendicular  to  the  direction  of  mag- 
netisation. We  may  therefore  obtain  a  diagram  showing  the 
true  surface  density  of  free  magnetism  on  the  actual  surface 
of  the  ellipsoid,  by  supposing  the  ellipsoid  shifted  through 
a  very  small  distance  in  the  direction  of  magnetisation,  so 
that  a  meniscus  is  formed  on  either  side  of  the  middle,  between 
the  old  and  the  new  positions.  Then  the  thickness  of  the 


FIG.  9. 

meniscus  is  proportional  to  the  surface  density  of  the  free 
magnetism.  Thus  in  Fig.  9  the  original  ellipsoid  is  C  A  C'  A'. 
By  shifting  it  through  the  small  distance  C  D  or  C'  D',  we  get 
the  positive  meniscus  C'  D',  which  is  a  diagram  of  the  surface 
density  of  positive  free  magnetism  on  one  half,  and  the  negative 
meniscus  C  D,  which  in  the  same  way  represents  the  negative 


FIG.  10. 

free  magnetism  on  the  other  half.  The  free  magnetism,  though 
densest  at  the  ends,  extends  towards  the  middle,  and  it  is 
only  at  the  equatorial  line  that  there  is  none.  It  is  easy 
to  show,  by  referring  to  the  geometrical  properties  of  an  ellip- 
soid, that  the  distribution  which  has  been  described  results  in 
making  the  total  quantity  of  free  magnetism  on  any  narrow 
zone  taken  perpendicular  to  the  direction  of  magnetisation 
proportional  to  the  width  of  the  zone  and  to  its  distance  from 


MOMENT   OP    ELLIPSOID.  27 

the  equator  A  A'.  In  other  words,  what  we  may  call  the  linear 
distribution  of  free  magnetism  in  the  direction  of  the  axis  C  C' 
is  correctly  represented  by  the  height  of  the  lines  above  and 
below  C  C'  in  Fig.  10. 

Again,  in  regard  to  linear  distribution,  it  follows  that  what  we 
may  call  the  centre  of  the  negative  magnetism  is  at  Q,  two-thirds 
of  the  distance  A  C  from  A,  and  the  centre  of  the  positive  mag- 
netism is  at  Q',  two-thirds  of  the  distance  A  C'  from  A.  The 

distance  Q  Q'  is  two-thirds  of  C  C',  or  -  c. 

3 

§  28.  Moment  of  Ellipsoid.  —  The  whole  quantity  of  positive 
or  of  negative  magnetism  is  TT  a2  I  —  namely,  I  multiplied  by 
the  area  of  the  equatorial  section,  which  is  a  circle  in  the 
special  case  we  have  taken,  the  case  of  an  ellipsoid  of  revolu- 
tion with  a  =  b.  On  distant  external  points  the  action  of  the 
magnetised  ellipsoid  will  be  the  same  as  if  this  quantity  of 
positive  magnetism  were  gathered  at  Q',  and  an  equal  quantity 
of  negative  magnetism  at  Q.  The  magnetic  moment  of  the 
ellipsoid  is  therefore 


But  we  might  have  obtained  this  result  more  directly.  Since 
I  is,  by  definition,  the  moment  per  unit  of  volume  (§  7),  and 

4  4 

the  volume  of  the  ellipsoid  is  -  IT  a2  c,  the  moment  is  -  IT  a?c  I, 

3  3 

as  above. 

§  29.  Application  to  the  Case  of  a  Sphere.  —  When  c  is 
equal  to  a,  the  eccentricity  e  is  0,  and  the  ellipsoid  becomes  a 
sphere.  We  then  have  the  case  of  which  Figs.  5  and  6  furnish 
illustrations.  The  sphere  is  uniformly  magnetised,  but  even 
when  the  material  of  which  it  is  made  is  exceedingly  permeable 
the  magnetisation  is  by  no  means  strong,  because  the  free  mag- 
netism which  becomes  developed  on  the  surface  causes  the  true 
magnetic  force  H  in  the  interior  to  be  much  less  than  the 
original  magnetic  force  H'  due  to  the  external  field. 

By  applying  the  general  formula  of  §  26  to  find  the  value  of 
N  in  the  expression 


28  MAGNETISM    IN    IRON 


it  may  be  shown  that  for  a  sphere  N  =  —  TT,  so  that 

9 

H-H'-^I. 

Dividing  by  H  we  have 

=  R~y7rlH  =  H  'Y77** 

Hence,  the  proportion  which  the  true  magnetic  force  H  bears 
to  the  force  in  the  undisturbed  field  is 

1=     _J_ 
H' 


This  shows  that  when  the  material  is  very  susceptible,  so 
that  K  is  large,  the  true  force  H  is  only  a  small  fraction  of  H'. 
To  take  a  practical  instance,  the  susceptibility  of  soft  iron  to 
weak  magnetic  forces,  such  as  those  produced  by  the  earth's 
field,  is  about  20.  Assigning  this  value  to  K,  we  have 

H       1 

—  =  —  approximately.  Thus  the  true  magnetic  force  within 
H  85 

a  spherical  ball  of  soft  iron  placed  in  the  earth's  field  is  only 
about  the  ¥Vth  part  of  the  force  in  undisturbed  parts  of  the 
field,  and  the  magnetisation  I  which  the  ball  will  take  up  is 
only  about  -yVth  of  that  which  would  be  taken  by  a  very  long 
rod  of  the  same  material  set  lengthwise  in  the  direction  of  the 
lines  of  terrestrial  magnetic  force. 

Again,  as  to  the  magnetic  induction  in  the  sphere  and  its 
relation  to  the  permeability,  we  have  (remembering  that  the 
permeability  />i  = 


When  p  is  exceedingly  large,  the  factor  —  iL  approximates  to 

3.  Hence,  in  a  sphere  of  very  permeable  material,  the  number 
of  lines  of  induction  through  the  sphere  (per  square  centimetre 
of  section)  is  nearly  three  times  the  number  of  lines  in  the 
undisturbed  field.  This  is  the  case  in  the  sphere  of  Fig.  6  (the 
proportion  of  the  closeness  of  the  lines  inside  to  that  of  the 
lines  outside  at  a  distance  from  the  sphere  being  J3  to  1,  as 
seen  on  the  plane  of  the  diagram).  The  student  should 


APPLICATION    TO   THE    CASE   OF    A  SHORT    ELLIPSOID.  29 

note  that  when  the  permeability  of  the  sphere  is  great, 
its  exact  value  has  very  little  influence  on  the  number  of 
lines  of  induction  that  pass  through  the  sphere,  and  hence 
a  spherical  ball  would  be  a  very  bad  form  of  body  to  select 
if  we  wished  by  measuring  the  induction  to  determine  the 
permeability  of  the  material.  A  small  error  in  the  form 
of  the  sphere  would,  in  fact,  have  more  influence  in  altering 
the  amount  of  the  induction  than  a  large  difference  in  the  value 
of  /A  or  of  K  ;  so  that,  as  Prof.  Chrystal  has  well  put  it,  the 
experimenter  would  be  testing  the  accuracy  of  his  instrument- 
maker  rather  than  the  magnetic  susceptibility  of  his  material.  * 

§  30.  The  same  objection  would  apply,  though  in  a  slightly 
less  degree,  to  a  short  ellipsoid.     By  way  of  illustrating  this 


Fio.  11.— Short  ellipsoid  of  infinitely  permeable  material  in  a  uniform  field. 

further,  Fig.  11  has  been  drawn  to  show  in  a  general  manner 
the  induction  through  an  ellipsoid,  and  the  distortion  which  it 
produces  in  an  originally  uniform  field,  when  the  axes  have  the 
proportion  of  4  to  1,  the  material  being  assumed  to  have 
indefinitely  great  permeability.  With  this  proportion  between 
the  axes,  jy,  by  the  formula  (1)  of  §  26,  is  0*946,  and  for  every 
line  of  force  (per  square  centimetre)  in  the  undisturbed  field 
there  are  13 '3  lines  of  induction  (per  square  centimetre)  within 
the  ellipsoid.  The  space  between  the  lines  within  the  body  is 
therefore  narrower  than  the  space  between  the  lines  in  any 
distant  part  of  the  field  in  the  proportion  of  1  to  J13'3.  The 
permeability  might  vary  widely  without  materially  affecting 

*  Article  "  Magnetism,"  Encyc.  JBritannica,  Ninth  Edition. 


30  MAGNETISM    IN    IROX. 

the  amount  of  induction,  and  the  figure  may  be  accepted  as 
representing  very  nearly  what  would  happen  if  the  ellipsoid 
were  of  soft  iron.* 

§  31.  Application  to  the  Case  of  a  Long  Cylindrical  Rod  of 
Circular  Section  Magnetised  Transversely  in  a  Uniform  Field.  — 

This  case,  of  which  an  example  is  furnished  by  a  long  wire 
stretched  in  the  earth's  field  in  a  direction  perpendicular  to  the 
lines  of  force,  is  deducible  from  the  general  case  of  the  ellipsoid 
by  making  one  of  the  axes  infinite.!  This  gives  JV=27r,  so 
that  H  =  H'-27r|. 

Hence,  M,  =  _  !  _  ,    and     ^-=^L. 

H      27TK  +  I*  H'    /*  +  ! 

Thus,  when  p  is  very  large,  as  it  is  in  soft  iron,  the  trans- 
verse induction  B  across  the  wire  approximates  to  a  value 
which  is  twice  that  of  the  external  field.  This  is  a  very  small 
induction  compared  with  that  which  the  same  wire  would 
take  longitudinally  if  it  were  set  lengthwise  instead  of  cross- 
wise in  the  field  (compare  §  15  above).  If  we  assume  K  to  be 
20,  the  proportion  of  the  induction  in  the  two  cases  is  about 
1  to  127. 

It  follows  from  this  that  when  we  hang  a  wire  vertically  in 
the  earth's  field,  the  transverse  magnetisation  due  to  the  hori- 
zontal component  of  the  earth's  field  is  so  small  that  account 

*  Generally,  to  find  the  proportion  of  the  induction  B  within  an  ellipsoid 
to  the  force  H'  in  the  undisturbed  field,  we  have  :  — 


~( 


When  the  permeability  of  the  substance  is  very  great,  the  expression 
within  brackets  approximates  to  ^,  giving  B=-^r  H'.  In  the  case  con- 
sidered  in  the  text,  —•  is  13'3. 

t  And  using  a  formula  (not  quoted  in  §  26)  which  refers  to  magnetisa- 
tion in  the  direction  of  an  equatorial  axis.    See  Maxwell,  loc.  cit. 


THIN    DISC   AND    LONG    ELLIPSOID.  31 

need  not  in  general  be  taken  of  it,  and  the  same  thing  is  true 
of  the  transverse  magnetisation  of  a  wire  laid  horizontally  in 
the  earth's  field. 

§  32.  Case  of  a  Thin  Disc  Magnetised  in  the  Direction  of  the 
Thickness  by  a  Uniform  Field.  —  We  may  find  the  true  mag- 
netic force  within  a  disc  or  large  thin  plate  magnetised  nor- 
mally in  a  uniform  field  from  the  fact  that  the  lines  of  induction 
B  within  the  disc  are  continuous  with  the  lines  of  force  H'  in 
external  space,  and  if  the  disc  is  very  wide  in  comparison  with 
its  thickness,  the  lines  go  straight  through  it  without  sensible 
distortion.  Thus  H'=B  =  47r|  +  H,  so  that  H  =  H'-47r|, 

H       I 

_-  =  —  ,  and  the  induction  within  the  disc  is  the  same  what- 

H'         /A 

ever  be  the  permeability  of  the  material.  The  same  result 
may  be  derived  from  equation  (3)  of  §  26,  by  making  a  inde- 
finitely great  in  comparison  with  c.  This  gives  e  =  \  and 


§  33.  Long  Ellipsoid  :  Influence  of  the  Length  on  the  Mag- 
netising Force.  —  Returning  now  to  the  general  case  of  a  long 
ellipsoid  of  revolution  placed  longitudinally  in  a  uniform  mag- 
netising field,  it  is  interesting  to  notice  to  what  extent  the 
uniform  magnetisation  of  the  ellipsoid  itself  affects  the  magnetic 
force,  when  we  assume  various  values  as  the  ratio  of  length 
(2  c)  to  transverse  diameter  (2  a). 

In  the  formula 


B-H 

we  may  write      ,        for  I  (by  §  13),  and  if  the  material  is  very 

permeable,  so  that  B  is  large  compared  with   H,  this  will  be 

p 
very  nearly  equal  to  —  simply.    Hence  in  an  ellipsoid  made  of 

4  7T 

very  permeable  material,  such  as  iron, 

N 
H  =  H'  -  ^  B,  very  nearly. 

The  following  values  of  .ZVand  also  of  j—  have  been  calcu- 
lated by  means  of  the  expressions  in  §  26  for  ellipsoids  in  which 


OF  THE 
t  i  *i  iv/CDClTV 


MAGNETISM    IN    [RON. 


the  ratio  of  length  to  breadth  is  f>0,  100,  200,  300,  400,  and 
500  respectively. 


Since  H  =  H'--flT  I, 


Ratio  of  Length  to 

N 

V 

Breadth  (£) 

47T 

50 

0-01817* 

0-001446 

100 

0-00540 

0-000430 

200 

0-00157 

0-000125 

300 

0-00075 

0-000060 

400 

0-00045 

0-000037 

500 

0-00030 

0-000024 

K-  +  1. 


The  proportion 

which  the  resultant  force  H  bears  to  the  original  force  H'  in 
the  undisturbed  field, 

HI 


By  the  help  of  the  above  table  it  is  easy  to  find  this  propor- 
tion, for  an  assigned  ratio  of  length  to  breadth,  when  the 
susceptibility  of  the  material  is  known. 

As  an  example,  we  may  take  K  =  200  as  a  representative 
value  of  the  susceptibility  in  soft  iron  when  subjected  to  a 
moderately  strong  magnetic  force.  Suppose  that  the  ellipsoid 
is  100  diameters  long,  then 

H  1  1 

H'     0-0054x200  +  1     2-08* 

In  other  words,  the  magnetic  force  actually  operative  within 
the  metal  —  as  reduced  by  the  magnetism  of  the  piece  itself  — 
is  in  that  case  rather  less  than  one  half  the  force  due  to  external 
causes. 

3  34.  Residual  Magnetism  and  Retentiveness.  —  When  a 
piece  of  any  one  of  the  strongly  magnetisable  metals  —  iron, 
steel,  nickel,  or  cobalt  —  is  magnetised  by  applying  magnetic 
force,  and  the  externally-applied  force  is  then  withdrawn,  it  is 
found  that  the  magnetisation  does  not  wholly  disappear.  What 

*  The  approximate  formula  (2)  of  §  26  gives  0'01812.  For  the  longer 
ellipsoids  the  values  of  N  calculated  from  it  may  be  taken  as  correct. 


SELF-DEMAGNETISING    FORCE.  33 

remains  is  usually  called  the  residual  magnetism,  and  metals 
which  retain  residual  magnetism  when  the  external  magnetic 
force  is  withdrawn  are  said  to  possess  retentiveness. 

We  shall  see  later  that  this  retention  of  residual  magnetism, 
when  the  externally  applied  magnetising  force  is  withdrawn,  is 
only  one  instance  of  a  general  tendency  which  these  metals 
exhibit  to  resist  any  change  in  their  magnetic  state. 

§  35.  Self-Demagnetising  Force. — In  connection  with  the 
subject  of  retentiveness  it  is  of  the  first  importance  to  notice 
that  though  the  externally  applied  magnetic  force  be  withdrawn 
from  a  magnetised  piece,  there  is  in  general  some  magnetic 
force  in  action.  This  force  is  due  to  the  residual  magnetism 
itself,  and  its  tendency  is  to  reduce  the  residual  magnetisa- 
tion. In  a  bar  magnet,  for  instance,  the  residual  magnetism  at 
and  near  the  ends  of  the  bar  produces  a  magnetic  force  acting 
in  the  direction  of  the  length  and  tending  to  demagnetise 
the  bar.  In  a  ring  magnet  uniformly  magnetised  we  get  rid 
of  this  self-demagnetising  force  by  having  the  ends,  so  to 
speak,  brought  together.  In  an  exceedingly  long  bar  the  self- 
demagnetising  force  becomes  insignificant  because  the  ends  are 
far  removed  from  most  parts  of  the  bar.  The  residual  mag 
netism  in  a  ring  or  a  very  long  rod  will  therefore  be  greater, 
other  things  being  equal,  than  in  a  short  rod.  Indeed,  so  much 
is  this  the  case  that,  in  dealing  with  soft  annealed  iron,  we  shall 
find  almost  no  residual  magnetism  if  we  experiment  with  rods 
the  length  of  which  is  only  10  or  20  times  their  diameter, 
because  in  these  rods  the  self-demagnetising  force  is  sufficient 
to  remove  the  residual  magnetism  almost  completely,  whereas  a 
rod  400  or  500  diameters  long  will  be  found  to  retain  a  very 
large  proportion  of  its  induced  magnetism  when  the  inducing 
force  is  withdrawn.  Hence  the  term  residual  magnetism  has 
one  meaning  when  it  is  used  to  describe  the  magnetism  that 
remains  when  magnetic  force  is  completely  withdrawn  without 
any  reverse  force  being  applied,  an  experiment  which  can  be 
made  if  we  use  an  exceedingly  long  rod  or  a  ring  magnet ;  and 
it  has  another  and  quite  different  meaning  when  it  is  used  to 
describe  the  magnetism  which  a  bar  or  other  short  piece  will 
retain  in  opposition  to  the  demagnetising  force  which  it  exercises 
upon  itself. 

D 


34  MAGNETISM   IN    IRON. 

§  36.  Self-Demagnetising  Force  in  Ellipsoids. — In  the  case 
of  an  ellipsoid,  uniformly  magnetised,  the  self-demagnetising 
force  is  uniform  throughout  the  body,  and  its  value  is 

yi, 

where  N  has  the  same  meaning  as  in  §  26,  and  I  is  the  residual 
intensity  of  magnetisation. 

To  get  an  idea  of  what  this  may  amount  to  in  actual  cases, 
we  may  take  1,000  C.-G.-S.  units  as  a  residual  value  of  I  which 
is  commonly  enough  found  in  the  magnetisation  of  iron. 
When  an  ellipsoid  is  200  times  as  long  as  it  is  broad  the  value 
of  Nia  0-00157  (by  §32),  and  a  residual  intensity  (I)  of  1,000 
would  therefore  produce  a  self -demagnetising  force  of  1-57. 
The  experimental  results  which  will  be  given  later  will  show 
that  a  force  of  this  magnitude  is  by  no  means  insignificant, 
and  that  it  would,  in  fact,  be  sufficient  to  remove  a  large  part 
of  the  residual  magnetisnVxJt  is  only  when  the  length  is  as 
much  as  400  or  500  times  the  transverse  diameter  that  the 
self-demagnetising  force  in  a  material  so  susceptible  as  iron 
becomes  nearly  negligible. 

The  factor  N  is  called  by  Prof.  H.  du  Bois  the  <r  factor  of 
demagnetisation."*  We  shall  see,  in  Chapter  X.,  that  a  factor 
of  the  same  character  applies  in  the  treatment  of  a  magnetic 
circuit  consisting  of  a  ring  with  an  air-gap,  and  also  how 
account  may  be  taken  graphically  of  the  factor  JV  in  dealing 
with  the  curves  showing  the  relation  of  magnetisation  to  mag- 
netising force. 


*  See  "  The  Magnetic  Circuit  in  Theory  and  Practice,"  by  Dr.  H.  du  Bois. 
(Longmans,  1896.) 


CHAPTER  II. 


MEASUREMENTS   OF  MAGNETIC   QUALITY:    THE 
MAGNETOMETRIC   METHOD. 

§  37.  Methods  of  Measuring  Magnetic  Quality. — From 
what  has  been  said  about  the  influence  which  the  ends  of  magne- 
tised bodies  exercise  by  reacting  on  the  magnetising  field,  and 
by  exerting  a  self-demagnetising  force  when  the  external  force 
is  withdrawn,  it  will  be  clear  that  when  we  attempt  to  measure 
the  permeability,  or  the  susceptibility,  or  the  retentiveness  of  a 
magnetic  metal,  we  must  either  arrange  the  conditions  of  the 
experiment  in  such  a  way  that  the  influence  of  the  ends  may 
be  calculated  and  allowed  for,  or  else  choose  pieces  which  are 
actually  or  practically  endless. 

We  may  use  long  ellipsoids  (short  ones  will  not  do,  for  the 
reason  already  explained — that  in  them  the  magnetisation 
depends  too  much  on  the  form  and  too  little  on  the  quality  of 
the  piece),  and,  having  observed  I,  calculate  the  true  magnetic 
force  within  the  metal  by  subtracting  N  \  from  the  externally 
applied  force  H'. 

Again,  if  the  piece  tested  is  a  very  long  cylindrical  rod  or  wire, 
the  influence  of  the  ends  may  be  approximately  allowed  for  by 
treating  the  piece  as  an  ellipsoid.  And  by  making  the  length 
great  enough  (400  times  the  diameter  or  so  if  iron  is  being 
tested  and  if  the  rod  is  straight)  we  may  reduce  the  influence 
of  the  ends  so  much  that  it  may  generally  be  neglected.  In 
a  rod  long  enough  to  be  practically  endless,  the  magnetic  force 
within  the  metal  is  sensibly  the  same  as  the  force  in  the  field 
when  the  rod  is  withdrawn  from  it. 

The  condition  of  endlessness  can  be  completely  secured  by 
giving  the  piece  to  be  magnetised  the  form  of  a  ring.  If 
we  take  a  ring  of  uniform  section,  and  wind  the  magnetising 


36  MAGNETISM    IN    IRON. 

coil  uniformly  all  round  it,  we  secure  a  magnetic  field  which  is 
uniform  throughout  the  length  of  the  ring,  and  nearly  uniform 
throughout  each  cross-section.  The  magnetic  force  operative 
on  the  metal  is  quite  independent  of  the  magnetism  of  the 
piece  itself.  The  ring  has  no  poles ;  it  does  not  react  on  the 
magnetising  field ;  and  when  the  external  force  is  withdrawn 
it  exerts  no  demagnetising  force  upon  itself. 

Ellipsoids,  long  rods,  and  rings  have  all  been  used  in  testing 
the  permeability  and  other  magnetic  qualities  of  iron.  Recent 
experiments  have,  as  a  rule,  been  made  either  with  rings  (or 
pieces  equivalent  to  rings),  or  with  very  long  cylindrical  rods. 
From  some  points  of  view,  long  ellipsoids  would  be  the  most 
satisfactory  of  all  forms  of  specimen,  but  the  difficulty  of 
shaping  them  correctly  is  a  serious  obstacle  to  their  use. 

§  38.  Classification  of  Methods :  Magnetometric  and 
Ballistic. — The  magnetisation  produced  in  a  specimen  by  apply- 
ing magnetic  force,  or,  more  generally,  the  change  of  magnet- 
ism produced  by  any  change  in  the  force,  is  usually  measured 
in  one  or  other  of  two  ways. 

In  one — the  magnetometric  method — the  magnetism  of  the 
piece  is  measured  by  observing  the  deflection  of  a  magnetic 
needle  suspended  near  it,  called  a  magnetometer.  This  method 
is  applicable  when  we  deal  with  ellipsoids  and  rods,  but  ob- 
viously cannot  be  used  with  rings,  since  a  uniformly  magnetised 
ring  exerts  no  magnetic  force  in  the  neighbouring  space. 

In  the  other  method,  any  change  in  the  magnetic  induction 
within  the  specimen  is  determined  by  measuring  the  transient 
current  which  is  induced  in  a  surrounding  coil  when  the  change 
of  induction  takes  place.  The  coil  acts  like  the  secondary 
wire  of  an  induction  coil  or  transformer.  When  any  change 
takes  place  in  the  number  of  lines  of  induction  surrounded  by 
the  coil,  a  transient  current  is  produced,  the  whole  quantity  of 
which  (that  is  to  say,  its  time-integral)  is  proportional  to  the 
change.  This  transient  current  is  measured  by  passing  it 
through  a  "  ballistic  "  galvanometer,  which  is  a  galvanometer 
with  a  needle  that  swings  slowly  enough  to  allow  practically 
the  whole  of  the  transient  current  to  pass  before  the  needle 
has  stirred  to  any  sensible  extent  from  its  position  of  rest.  This 
"  ballistic  "  method  is  applicable  to  rings  as  well  as  to  rods  of 


MAGNETOMETRIC   METHOD.  37 

any  form,  and  is  in  fact  the  only  method  by  which  we  may 
examine  the  magnetic  quality  of  a  ring.  When  applied  to  rings 
it  serves  to  measure  sudden  changes  of  magnetism  only,  such 
as  may  be  caused  by  making,  breaking,  reversing,  or  suddenly 
increasing  or  reducing  the  current  in  the  magnetising  coil. 
When  applied  to  rods  the  ballistic  method  may  be  modified,  so 
that  it  will  measure  the  actual  magnetic  state  of  the  piece, 
and  not  sudden  changes  merely.  This  is  done  by  winding  the 
secondary  coil  in  such  a  way  that  it  may  be  suddenly  slipped 
off  the  magnetised  piece,  and  removed  far  enough  from  it  to  be 
out  of  the  reach  of  magnetic  influence,  remaining,  however,  all 
the  while  in  circuit  with  the  ballistic  galvanometer.  Slipping 
off  the  coil  gives  a  transient  current  which  corresponds  to  the 
sudden  removal  of  all  the  lines  of  induction. 

We  shall  now  describe  the  two  methods  in  some  detail,  and 
give  examples  of  their  application. 

§  39.  Magnetometric  Method. — In  this  method  the  rod  or 
other  piece  whose  magnetisation  is  to  be  measured  is  fixed  near 
the  magnetometer,  the  needle  of  which  is  already  directed  by 
some  known  magnetic  force.  Generally,  the  needle  hangs 
horizontally  under  the  control  of  the  earth's  magnetism  alone, 
so  that  the  directing  force  is  the  horizontal  component  of  the 
earth's  magnetic  field.  The  magnetised  piece  is  fixed  in  such 
a  position  that  the  magnetic  force  which  it  produces  at  the 
magnetometer,  or  what  we  may  call  the  deflecting  force,  acts 
at  right  angles  to  the  directing  force.  The  tangent  of  the 
angle  of  deflection  then  measures  the  proportion  of  the  deflect- 
ing to  the  directing  force.  Thus,  in  Fig.  12,  if  the  magnetised 
body  is  placed  so  that  it  produces  a  magnetic  force  F2  at  the 
magnetometer  needle  a  &,  and  the  directing  force  is  Fx,  the 
needle,  which  originally  pointed  in  the  direction  of  Fv  is 
deflected  through  an  angle  6  such  that 

F2  =  Fj  tan0. 

Knowing  F1  and  observing  0,  we  determine  F2,  and  from 
that,  knowing  the  position  and  dimensions  of  the  magnetised 
piece,  we  calculate  its  intensity  of  magnetisation. 

Suppose,  for  instance,  that  the  magnetic  bar  is  an  ellipsoid  of 
revolution  (with  polar  axis  2  c  and  equatorial  axes  2  a)  placed  in 


58 


MAGNETISM  IN  IRON. 


the  position  shown  by  the  line  C  C'  in  Fig.  13.  The  bar  lies  hori- 
zontally, level  with  the  magnetometer  needle  0,  which  is  opposite 
the  middle  of  the  bar  and  points  to  it  when  in  the  undeflected 


FIG.  12. 


\ 


FIG.  13. 


position.    In  its  action  on  a  distant  point*  the  ellipsoidal  bar  is, 

*  It  is  only  when  the  point  0  is  at  a  considerable  distance  from  C  C ' 
that  the  effect  of  the  bar's  distributed  magnetism  is  approximately  the 
same  as  that  of  poles  at  Q  and  Q '.  If  O  is  near  the  bar,  the  formula  in 


MAGNETOMETRIC    METHOD.  39 

as  we  have  seen  in  §  27,  equivalent  to  a  positive  pole  of  strength 
IT  a2  I  at  Q  and  an  equal  negative  pole  at  Q',  the  distance  Q  Q' 

being  -  c.     The  deflecting  force  F2  which  the  bar  produces  at 
3 

the  magnetometer  is  the  resultant  of  the  equal  forces 

7T  Cb     I  T          7T  d     I 

-=-  and  —  _==- 
OQ2  OQ'2 

Its  direction  is  parallel  to  the  bar,  and,  as  the  diagram  shows, 

F2:=<!::QQ':OQ, 

TT  ct2 1  0,  Q'     4  TT  a? 


or 


F                              _.____. 
O  ==  —  Q 

0  Q3  3  0  Q3 


And,  since  F2  =  Fx  tan  0,  we  may  put  this  result  in  the  follow- 
ing form,  suitable  for  finding  the  intensity  of  the  bar's  mag- 

netisation :  — 


_ 

4  TT  a*  c 

§  40.  Magnetometric  Method  (continued).  —  Another  position 
for  the  specimen  to  be  magnetised  is  shown  in  Fig.  14.  The 
plane  of  the  sketch  is  vertical.  0  is  the  magnetometer,  the 
needle  of  which,  when  undeflected,  points  at  right  angles  to  the 
plane  of  the  paper.  The  bar  is  fixed  behind  it,  standing  ver- 
tically with  its  upper  pole  at  the  level  of  the  magnetometer. 
The  deflecting  force  F2  is  mainly  due  to  the  upper  pole  :  its 
value  is  — 

7ra2l       X7T  q2  |\  Q  Q       va*  \    f       _  /Q  Q 

OQ2      VW^oQ7~~OQ2   '        ^°Q/ 
And  since  this  is  equal  to  Fl  tan  6,  we  have 

_         QQ2  F!  tan  B 


the  text  is  not  applicable  ;  but  it  is  in  any  case  practicable  to  calculate  the 
deflecting  force  at  0,  since  the  distribution  of  free  magnetism  along  C  0* 
is  known. 


40 


MAGNETISM   IN   IRON1. 


This  arrangement  is  particularly  applicable  where  we  have 
to  deal  with  a  very  long  cylindrical  rod  (diameter  2  a).  In 
such  a  rod  the  position  of  the  effective  poles  Q  and  Q'  is 
uncertain,  and,  indeed,  varies  when  the  intensity  of  magnetisa- 
tion is  varied.  But  the  method  has  this  advantage,  that  a 
change  in  the  position  of  Q  along  the  rod  produces  very 
little  change  in  its  distance  from  the  magnetometer,  and  has 
little  effect  in  altering  the  deflecting  force,  while,  as  to  the 
other  pole  Q',  its  total  effect  is  so  small  that  a  movement  of  it 
is  also  without  much  influence.  The  best  height  at  which  to  set 
the  rod  will  be  found  by  giving  it  a  moderate  degree  of  mag- 


FIG.  14. 


netisation,  and  finding  by  trial  how  high  the  upper  end  should 
stand  above  the  level  of  the  magnetometer  to  make  the  deflec- 
tion a  maximum.  In  this  way  the  position  of  Q,  and  therefore 
of  Q'  also,  may  be  found  with  sufficient  accuracy  to  allow  the 
formula  to  be  applied  to  a  very  long  cylinder.  For  brevity,  we 
may  distinguish  this  as  the  "  one-pole  "  method,  seeing  that  the 
deflection  of  the  magnetometer  is  mainly  caused  by  one  of  the 
bar's  poles. 

§  41.  Details  of  Magnetometric  Method. — A  form  of  mag- 
netometer, which  is  exceedingly  convenient  for  observations  of 
this  kind,  and  can  be  made  by  anyone  at  a  very  trifling  cost, 


DETAILS    OF    MAGNETOMETRIC    METHOD. 


41 


is  shown  in  Fig.  15.  The  suspended  "needle"  consists  of 
one  of  the  mirrors  used  in  Lord  Kelvin's  reflecting  galva- 
nometers, with  small  magnets  cemented  on  the  back.  The 
mirror  M  is  hung  from  a  pin,  S,  at  the  top  of  a  wooden  upright, 
by  a  silk  fibre  three  or  four  inches  long.  A  groove  is  cut  in 
the  upright  to  allow  the  fibre  to  hang  free,  and  at  the  bottom 
a  round  hole,  closed  in  front  by  a  lens,  forms  a  chamber  in 
which  the  mirror  hangs.  A  glass  plate  is  cemented  on  the 
back  of  the  upright  to  cover  the  hole  and  the  groove.  The 
upright  is  fixed  to  a  horizontal  plate  furnished  with  three 
levelling  screws.  The  deflection  of  the  mirror  is  read  in  the 
usual  way  by  means  of  a  lamp  and  scale. 


FIG.  15. 

In  using  a  mirror  magnetometer,  the  angle  through  which 
the  needle  is  deflected  may  generally  be  kept  so  small  that  no 
account  need  be  taken  of  the  difference  between  tan  0  and  0, 
and  consequently  the  scale  readings  may  be  taken  as  propor- 
tional to  the  deflecting  forces.  Thus,  if  we  have  a  scale  50cm. 
long,  set  one  metre  from  the  magnetometer,  a  deflection  of  the 
needle  amounting  to  only  about  7deg.  will  make  the  spot  of 
light  travel  from  the  middle  to  the  end  of  the  scale.  (It  must 
be  remembered  that  the  angular  deflection  of  the  mirror  is  only 
half  that  of  the  beam  of  light.)  Even  for  this  largest  deflection 
the  error  caused  by  taking  scale  divisions  instead  of  tangents 
is  barely  a  half  of  one  per  cent.,  and  for  smaller  deflections  the 
error  is  very  much  less.  In  such  a  case,  therefore,  instead  of 


42  MAGNETISM   IN   IRON. 

c> 

tan  0  we  may  write  0,  'which  is  equal    to  ,  8   being  the 

deflection  as  measured  on  the  scale,  and  D  the  distance  of  the 
scale  from  the  mirror  expressed  in  scale  divisions. 

Fig.  16  illustrates  an  arrangement  for  examining  the  mag- 
netic quality  of  long  thin  rods  or  wires  by  the  "  one-pole  " 
variety  of  the  magnetometric  method.  The  specimen  is  slipped 
into  a  tube,  A,  which  is  clamped  in  a  vertical  position  behind 
the  magnetometer  B,  the  distance  being  adjusted  by  trial  to 
make  the  deflection  conveniently  large.  Over  the  tube  a 
magnetising  solenoid  is  wound,  extending  a  little  way  above 
and  below  the  wire  core,  so  that  the  magnetising  force  inside 
may  be  sensibly  uniform,  except  in  so  far  as  it  is  affected  by 
the  ends  of  the  specimen  itself.  (When  only  one  wire  is  to  be 
tested,  the  magnetising  solenoid  may  conveniently  enough  be 
wound  on  the  wire  itself,  instead  of  on  a  tube.)  Owing  to  the 
vertical  position  of  the  specimen,  it  is  exposed  to  the  vertical 
component  of  the  earth's  magnetic  force.  For  many  purposes 
it  is  desirable  to  eliminate  this,  so  that  the  only  force  acting 
along  the  wire  may  be  that  due  to  the  magnetising  solenoid. 
To  secure  this  a  second  solenoid  is  wound  upon  the  tube,  and 
through  it  a  constant  current  is  kept  up,  the  strength  of  which 
is  adjusted  (by  a  method  to  be  described  later)  until  the  mag- 
netic force  it  produces  within  the  tube  just  balances  the  earth's 
vertical  force.  In  the  sketch,  the  single  gravity  Daniell  cell  C 
and  the  resistance  box  D  give  the  means  of  maintaining  and 
regulating  this  constant  current. 

In  circuit  with  the  main  solenoid  and  behind  the  specimen 
is  a  coil,  E,  consisting  of  a  few  turns  of  wire  wound  on  a 
wooden  frame  which  can  slide  towards  or  from  the  magneto- 
meter, its  axis  passing  through  the  magnetometer  at  right 
angles  to  the  undeflected  direction  of  the  needle.  This  "  com- 
pensating coil,"  as  we  shall  call  it,  serves  to  neutralise  the 
direct  action  of  the  magnetising  solenoid  upon  the  magneto- 
meter. Its  position  is  adjusted  thus  :  Before  putting  the  speci- 
men to  be  magnetised  into  the  magnetising  solenoid,  pass  a 
fairly  strong  current  through  the  solenoid  and  the  compensat- 
ing coil,  and  push  the  coil  backwards  or  forwards  until  the 
magnetometer  shows  no  deflection.  The  adjustment  remains 
correct  for  all  currents,  and  its  effect  is  that  when  the  specimen 


DETAILS   OP   MAGNETOMETRIC    METHOD. 


43 


44  MAGNETISM    IX   IRON. 

is  put  in  no  deduction  has  to  be  made  from  the  observed 
deflection  on  account  of  the  magnetising  solenoid. 

We  may  of  course  allow  for  the  effect  of  the  solenoid  without 
using  a  compensating  coil,  by  observing  what  deflection  the 
solenoid  itself  produces  with  a  given  strength  of  current  when 
the  specimen  is  removed,  and  then  making  a  proportional 
deduction  for  other  currents.  The  compensating  coil,  however, 
has  a  great  advantage  over  this  in  point  of  practical  convenience, 
and  has  other  uses  besides,  of  which  examples  will  be  given 
later. 

In  each  part  of  the  connections  the  leading  wires  are  twisted 
together — a  very  necessary  precaution  to  prevent  their  acting 
on  the  magnetometer. 

In  examining  the  permeability  of  a  specimen,  a  weak  mag- 
netising current  is  first  applied,  and  this  is  increased  step  by 
step  or  continuously,  observations  of  the  current  strength  being 
taken  along  with  observations  of  the  magnetometric  deflection. 
A  storage  battery  forms  the  most  convenient  source  of  current ; 
if  that  is  not  available,  a  battery  of  gravity  Daniell  cells  will 
do  well.  To  observe  the  current  strength,  any  good  form  of 
galvanometer  or  ampere-meter  may  be  kept  in  circuit  with 
the  magnetising  solenoid.  A  plan  which  is  as  good  as  any  is  to 
use  a  low-resistance  mirror  galvanometer,  strongly  controlled 
by  a  fixed  permanent  magnet,  and  test  its  sensibility  by 
passing  a  current  through  it  from  a  gravity  Daniell  cell ;  the 

strength  of  the  current  in  amperes  may  be  taken  as  -— ,  where 

.  Iv 

R  is  the  total  resistance  of  the  circuit  in  B.A.  units.  Care  must 
be  taken  to  set  up  the  galvanometer  far  enough  away  from  the 
magnetometer  to  prevent  one  from  acting  on  the  other. 

In  many  magnetic  experiments  it  is  desirable  to  have  the 
means  of  altering  the  magnetising  current  continuously  instead 
of  by  steps,  between  zero  and  its  highest  value.  This  is  con- 
veniently effected  by  using  the  liquid  rheostat,  or  potential 
slide,  shown  in  Fig.  17.  A  tall  glass  jar  of  fairly  uniform  bore, 
two  inches  or  so  in  diameter,  is  filled  with  dilute  solution  of 
sulphate  of  zinc.  Three  blocks  of  amalgamated  zinc,  cr,  b,  and 
c,  are  fitted  in  the  jar,  one  lying  at  the  bottom,  another 
fired  at  the  top,  and  the  third  hung  between  them  so  that 
it  may  be  raised  or  lowered  by  the  cord  d  which  passes 


DETAILS   OF   MAGNETOMETRIC   METHOD. 


45 


over  a  pulley  above  to  the   little   winch   at  e.     The  blocks 
are  connected  to  three  terminals  at  /,  insulated  wires  being 


FlG.  17. — Liquid  rheostat  used  for  the  purpose  of  continuously  altering 
the  strength  of  the  iiiagnetising  current. 


FIG.  18. 

led    up    through    the    liquid    from    the    middle    and    lowei 
blocks.     The  battery  is  connected  to  a  and  c,  so  that  the  liquid 


46  MAGNETISM    IN    IRON. 

column  forms  a  shunt  to  it,  and  a  part  of  its  E.M.F.  is  taken  ofl 
to  produce  current  in  the  magnetising  solenoid  by  connecting 
the  ends  of  the  solenoid  to  one  of  the  fixed  and  one  of  the  mov- 
ing blocks,  say  a  and  b.  Thus,  when  b  is  raised  into  contact 
with  a  no  current  passes  through  the  solenoid,  and  when  b  is 
gradually  lowered  the  current  increases,  reaching  its  highest 
value  when  b  touches  c.  With  this  slide  it  is  easy  to  adjust  the 
current  to  any  intermediate  value,  and  to  keep  it  constant  for 
as  long  as  may  be  wished. 

Fig.  18  is  a  general  diagram  of  the  connections.  The  letters 
A,  B,  C,  D  and  E  refer  to  the  same  parts  as  in  Fig.  16.  F  is  a 
revolving  commutator,  G  a  galvanometer  for  measuring  the 
magnetising  current,  and  H  is  the  slide  described  above. 

§  42.  Demagnetising  by  Reversals. — The  liquid  slide  gives 
a  handy  means  of  performing  a  process  which  is  resorted  to 
when  we  wish  to  rid  the  specimen  of  any  initial  magnetism 
it  may  possess,  or  to  wipe  out  the  residual  effects  of  previous 
operations.  The  process  of  "demagnetising  by  reversals" 
consists  in  applying  a  numerous  series  of  magnetic  forces 
alternating  in  direction,  and  gradually  diminishing  to  zero. 
A  commutator  or  rapid  reversing  key  is  inserted  either  between 
the  battery  and  the  slide  or  between  the  slide  and  the  mag- 
netising solenoid.  Working  it  rapidly  with  one  hand,  and  turning 
the  winch-handle  of  Fig.  17  very  slowly  with  the  other,  the 
operator  applies  a  long  series  of  alternating  magnetising  currents, 
each  a  very  little  weaker  than  the  one  before  it,  and  the  result 
is,  when  the  process  is  carefully  conducted,  to  remove  all  trace 
of  residual  magnetism,  provided  the  strongest  current  of  the 
series  is  at  least  as  strong  as  the  current  by  which  the  piece 
had  been  previously  magnetised. 

§  43.  Adjustment  of  the  Current  Required  to  Balance  the 
Vertical  Component  of  the  Earth's  Field. — The  operation  of 
demagnetising  by  reversals  will  not  be  completely  successful 
unless  the  earth's  vertical  force  is  very  exactly  balanced,  other- 
wise there  will  be  a  one-sidedness  in  the  alternate  opposite 
magnetic  forces,  which  will  show  itself  by  leaving  a  persistent 
residue  of  magnetism  in  one  direction  or  the  other,  the  direc- 
tion depending  on  whether  the  constant  current  which  is  applied 


TO    FIRD    DIRECTING    FORCE   AT   MAGNETOMETER.  47 

to  balance  the  earth's  force  is  too  strong  or  too  weak.  This 
affords  an.  excellent  criterion  by  which  we  may  adjust  the 
current.  It  has  to  be  strengthened  or  weakened  until,  when 
the  process  of  demagnetising  by  reversals  is  performed,  the  de- 
magnetisation is  complete.  The  more  susceptible  the  material 
within  the  solenoid  is,  the  more  sensitive  is  the  test,  and  it  is 
well  to  keep  at  hand,  for  the  purpose  of  adjusting  the  current 
in  this  way,  a  core  of  soft  annealed  iron,  which  may  be 
slipped  into  the  solenoid  when  the  test  is  to  be  made.  In  order 
to  increase  the  sensibility  further,  when  a  fine  adjustment  is  re- 
quired, the  solenoid  should  be  set  a  good  deal  closer  to  the 
magnetometer  than  it  is  set  when  we  are  afterwards  measuring 
the  magnetism  of  a  wire  or  rod  within  it. 

§  44.  To  Find  the  Directing  Force  at  the  Magnetometer. — 

In  measuring  magnetism  by  the  magnetometric  method,  we 
must  know  the  force  F:  which  directs  the  needle  when  it 
hangs  in  the  undeflected  position.  Even  when  no  special 
directing  magnets  are  used,  it  is  not  safe  to  assume  that  Fj  is 
identical  in  value  with  the  horizontal  component  of  terrestrial 
magnetism,  for  the  earth's  field  is  often  seriously  altered  within 
a  room  by  the  magnetic  influence  of  iron  pipes,  beams,  and  so 
forth.  So  long  as  these  disturbing  bodies  are  not  liable  to  be 
moved  about,  or  to  have  their  temperature  much  altered,  their 
effect  in  modifying  the  magnetic  field — though  it  may  be  con- 
siderable— will  be  nearly  constant,  and  in  that  case  an  occa- 
sional measurement  of  Fj  will  suffice.  If  there  are  iron  heating 
pipes  or  stoves  in  the  neighbourhood,  the  utmost  care  is  neces- 
sary to  see  that  Fx  does  not  vary.  Fixed  masses  of  iron  at  the 
atmospheric  temperature  are  not  a  very  objectionable  feature 
in  a  magnetic  laboratory ;  but  it  is  difficult  to  exaggerate  the 
nuisance  that  may  be  caused  by  an  iron  stove  or  steam-pipe 
liable  to  quick  changes  of  temperature. 

We  may  make  an  entirely  independent  measurement  of  Fx, 
following  the  well-known  method  which  is  used  in  measuring  the 
horizontal  component  of  the  earth's  field,*  and  taking  care  to 


*  Full  directions  for  the  determination  of  the  horizontal  component  ol 
the  earth's  field  will  be  found  in  Prof.  A.  Gray's  "  Absolute  Measurements 
in  Electricity  and  Magnetism." 


48  MAGNETISM    IN    IRON. 

swing  the  deflecting  magnet  in  th<3  place  where  the  magneto- 
meter is  to  stand. 

But  in  general  all  that  is  required  is  to  go  through  as  much 
of  this  process  as  will  serve  to  find  the  relative  values  of  Fl 
and  the  horizontal  field  F  at  a  place  where  there  is  no  local 
magnetic  disturbance.  In  most  places  F  is  sufficiently  well 
known  from  the  results  of  recent 'magnetic  surveys,  so  that 
the  absolute  value  of  Fj  may  be  deduced  when  we  know  the 
ratio  it  bears  to  F. 

To  compare  the  two,  take  a  short  straight  piece  of  perma- 
nently magnetised  steel  wire,  and  suspend  it  to  hang  hori- 
zontally within  a  glass  vessel  by  a  little  cradle  and  a  silk  fibre 
3in.  or  4in.  long  attached  to  the  cover,  so  that  it  is  free  to  swing. 
Put  it  where  the  magnetometer  is  to  stand,  and  set  it  swinging 
torsionally  (not  in  pendulum  fashion).  This  is  most  easily  done 
by  bringing  a  bar  magnet  near  it,  and  then  drawing  that  away, 
keeping  the  two  poles  of  the  bar  equally  distant  from  the  hang- 
ing wire.  When  the  swings  have  subsided  so  that  the  motion 
is  no  more  than  5deg.  or  so  to  either  side,  begin  to  count  them. 
Note  with  a  watch  the  instant  at  which  the  magnet  swings 
past  its  middle  position  towards  one  side,  count  30  or  40  com- 
plete swings,  and  again  note  the  time  the  magnet  swings 
past  its  middle  position  towards  the  same  side.  Find 
in  this  way  the  time  ^  (in  seconds)  required  for  one 
complete  swing.  Then  take  the  swinging  magnet  to  some 
place  (outside)  where  there  is  nothing  to  interfere  with  the 
terrestrial  magnetic  field,  and  repeat  the  counting  there 
to  find  the  time  that  is  required  to  make  one  complete  swing 
when  the  only  directing  force  is  the  horizontal  component  F  of 
the  earth's  field.  The  directing  force  is  inversely  proportional 
to  the  square  of  the  period  of  swinging,  hence  the  directing 
force  at  the  place  where  the  swings  were  first  counted 

F  =  — 

When  the  magnetometer  is  furnished  with  a  "  compensating 
coil"  (§  41)  the  following  is  a  good  way  to  find  Fr  Remove 
the  magnetising  solenoid  and  set  the  compensating  coil  at  a 
known  distance,  0  A  (Fig.  19),  behind  the  magnetometer.  Pass 


TEST   OF    IRON    BY    THE    MAGNETOMETRIC    METHOD. 


49 


a  known  current,  C,*  through  it  and  observe  the  deflection 
6  of  the  magnetometer.  A  B  is  the  mean  radius  of  the  coil, 
and  0  A  is  measured  to  the  middle  of  its  width.  Let  q  be  the 
number  of  turns  in  the  coil ;  then  the  deflecting  force  which 
is  produced  at  0  by  the  current  in  the  coil  is 


or 


(KB3 


and,  since  this  is  equal  to  Fx  tan  0,  we  have 


0  B3  tan  0 


FIG.  19. 


§  45.  Example  of  a  Test  of  Iron  by  the  Magnetometric 
Method. — Before  proceeding  to  describe  the  ballistic  method 
of  measuring  magnetisation,  it  may  be  useful  to  illustrate  the 
magnetometric  method  by  giving  the  particulars  of  an  actual 
experiment  on  a  piece  of  wrought-iron  wire. 

The  diameter  of  the  wire  (d)  was  0-077  cm.  The  length 
of  the  specimen  was  30 -5  cms.,  or  400  diameters.  It  was 
annealed  or  softened  before  the  test  by  drawing  it  through  a 
lamp  flame  so  slowly  that  each  part  of  the  length,  in  succes- 
sion, was  heated  to  bright  redness  and  then  cooled  slowly  as  it 
passed  away  from  the  flame.  The  "  one-pole"  arrangement  (§40) 
was  adopted.  A  preliminary  trial  showed  that  the  effective 
"  poles  "  lay  very  near  the  ends  of  the  wire.  The  upper  one  was 
set  at  a  distance  (0  Q)  of  10  cms.  behind  the  magnetometer  • 
the  distance  0  Q'  to  the  lower  pole  was  31  cms. 

*  Here,  as  elsewhere,  the  current  is  expressed  in  absolute  electro- 
magnetic (C.-G.-S.)  units.  If  its  value  is  known  in  amperes  we  must 
divide  the  number  of  amperes  by  10  to  find  C, 


50  MAGNETISM    IN    IRON. 

The  directing  force  at  the  magnetometer  Fj  was  0-299  in 
C.-G.-S.  units.  The  deflections  were  read  in  millimetres,  and 
the  scale  was  set  at  a  distance  of  1  metre  from  the  magneto- 
meter. Hence  one  scale  division  of  deflection  corresponds  to 
a  value  of  -^Vrr  for  6  or  tan  0. 

Substituting  these  values  in  the  expression  of  §  40, 

,  4.QQ2.  FJ  tan 0 

= 


we  have  I  for  one  scale  division  of  magnetometer  deflection 

4  x  io2  x  0-299 
__  ^ •Lvy =3'32 

3-1416  x  OK)772  x  0-9665  x~2000 

Again,  the  magnetising  solenoid  contained  69  turns  per 
centimetre  of  its  length.  Its  magnetising  force  for  one  ampere 
of  current  was,  therefore, 

47rx69_86.7 
10 

The  current  was  measured  by  a  mirror  galvanometer,  which 
was  found  to  give  a  deflection  of  575  scale  divisions,  with  a 
current  of  0-235  amperes.  This  corresponds  to  0-000408 
amperes  per  scale  division.  Hence  the  magnetising  force  for 
one  scale  division  of  the  galvanometer  was 

867  x -000408  =  0-0354. 

After  the  independent  current  (in  a  separate  solenoid)  which 
was  required  to  balance  the  vertical  component  of  the  earth's 
force  had  been  adjusted,  the  process  of  demagnetising  by 
reversals  was  gone  through  to  wipe  out  any  traces  of  magnetism 
the  wire  might  have  acquired  in  handling.  Readings  of  the 
magnetometer  and  galvanometer  were  then  taken,  while  the 
current  was  slowly  increased  step  by  step  from  zero  till  the 
magnetic  force  reached  a  value  of  22*27  units.  Then  the 
turrent  was  slowly  and  step  by  step  reduced  to  zero,  the  mag- 
netism retained  by  the  specimen  being  observed  at  each  stage, 
and  then  a  negative  current  was  applied,  giving  a  reversed 
magnetic  force,  which  was  slowly  increased  until  the  residual 


MAGNETISATION    OF   ANNEALED    IRON    WIRE. 


51 


magnetism  began  to  become  reversed.  The  results  of  the 
experiment  are  stated  in  Ta.ble  I.  Column  1  gives  the  ob- 
served galvanometer  deflections,  and  column  2  the  magnetising 
force  calculated  from  them.  This  is  the  force  produced  by  the 
solenoid;  in  the  notation  of  §25  it  is  H',  and  is  a  little  greater 
than  the  true  magnetic  force  H,  which  is  diminished  by  the 
action  of  the  ends  of  the  specimen  when  it  becomes  magnetised 
(see  §  47  below).  Column  3  gives  the  observed  magnetometer 
deflections  (due  to  the  wire  alone),  and  column  4  gives  values 
of  I  calculated  from  them. 

TABLE  I. — Magnetisation  of  Annealed  Iron  Wire. 


(1) 

Magnetising  cur- 
rent (Gal.  readings). 

(2) 
Magnetising 
Force. 

(3) 
Magnetometer 
Readings. 

(4) 

1 

0 

0 

0 

0 

9 

0'32 

1 

3 

24 

0-85 

4 

13 

39 

1-38 

10 

33 

59 

2-18 

28 

93 

79 

2-80 

89 

295 

99 

3-50 

175 

581 

119 

4-21 

239 

793 

139 

4-92 

279 

926 

159 

5-63 

304 

1,009 

189 

6-69 

327 

1,086 

239 

8-46 

348 

1,155 

289 

10-23 

359 

1,192 

342 

12-11 

365 

1,212 

441 

15-61 

373 

1,238 

574 

20-32 

378 

1,255 

629 

22-27 

380 

1,262 

464 

16-42 

379 

1,258 

239 

8-46 

375 

1,245 

139 

4-92 

372 

1,235 

89 

3-15 

369 

1,225 

39 

1-38 

363 

1,205 

0 

0 

350 

1,162 

-  11-5 

-0-41 

342 

1,135 

-   23 

-0-81 

329 

1,092 

-  31 

-1-10 

318 

1,056 

-   41 

-1-45 

295 

979 

-  51 

-1-80 

253 

840 

-   62 

-2-20 

166 

551 

-  71 

-2-51 

70 

232 

-   81 

-2-87 

-12 

-40 

52  MAGNETISM   IN   IRON. 

§  46.  Magnetisation  Curve. — A  convenient  way  of  repre- 
senting such  results  graphically  is  to  draw  a  curve  showing 
the  relation  of  the  magnetising  force  to  I  or  to  B.  In  Fig.  20 
a  curve  showing  the  relation  of  the  magnetising  force  of  the 
solenoid  to  I  is  drawn  from  the  above  table.  0  A  B  is  the 
ascending  limb,  got  by  applying  and  increasing  a  magnetising 
current,  the  iron  being  originally  in  a  non-magnetised  and  per- 
fectly neutral  state.  From  B  to  C  the  magnetising  current  is 
being  reduced  to  zero;  from  C  to  D  an  increasing  negative 
current  is  being  applied. 

This  example  is  thoroughly  characteristic  of  the  behaviour 
of  annealed  wrought  iron.  The  ascending  limb  of  the  curve  may 
be  divided,  broadly,  into  three  portions.  In  the  first,  under 
feeble  magnetic  forces,  the  gradient  of  the  curve  is  very  small, 
which  means  that  at  this  stage  there  is  (comparatively)  very 
little  magnetic  susceptibility.*  Later,  as  the  force  increases, 
the  curve  becomes  exceedingly  steep,  and  nearly  straight ;  this 
is  the  region  of  great  susceptibility.  Then,  lastly,  the  curve 
rounds  off  until  the  rate  of  ascent  again  becomes  small,  so  that 
the  susceptibility  diminishes,  and  any  considerable  addition  to 
I  can  then  be  brought  about  only  by  applying  a  very  strong 
magnetising  force. 

This  third  stage  is  a  necessary  consequence  of  the  well- 
known  phenomenon  of  magnetic  "  saturation."  We  shall  see 
later  that  the  value  of  I  has  a  definite  limit  which  cannot  be 
exceeded  no  matter  how  high  the  magnetic  force  be  raised. 

§  47.  Residual   Magnetism   and   Coercive   Force. — In  the 

descending  limb  of  the  curve  it  is  interesting  to  notice  how 
little  of  the  magnetism  disappears  as  the  magnetic  force  is 
withdrawn.  Even  when  the  solenoid  current  is  reduced  to 
zero,  the  residual  magnetism  0  C  is  in  this  case  1,162  C.-G.-S. 
units,  which  is  no  less  than  92  per  cent,  of  the  value  reached 
when  the  current  was  in  action  (1,262  units).  This  residual 
magnetism  is,  however,  very  feebly  held.  Applying  a  reverse 

*  The  comparatively  small  susceptibility  of  iron  to  feeble  forces  seems 
to  have  been  first  clearly  pointed  out  by  Stoletow  (Phil.  Mag.,  Vol.  XLV., 
1873,  p.  40),  whose  observations  on  the  relation  of  magnetisation  to  mag- 
netic force  were  confirmed  and  greatly  extended  by  Rowland  (Phil.  Mag.t 
Vol.  XLVL,  1873,  p.  140  j  and  Vol.  XLVIIL,  1874,  p.  321). 


uoiJESijauBew      o      jisuajui 
°        o        o  •     -o      ^b  *     o-       o1       o 
gooooooo 
°ff>^<om  * 


o 
oS 


54  MAGNETISM  IN  IRON. 

magnetic  force  quickly  removes  it,  as  the  continuation  C  D  of 
the  descending  limb  shows,  and  a  force,  0  D,  of  -  2 '75  C.-G.-S. 
units  suffices  to  destroy  it  altogether.  This  force  0  D  may  be 
said  to  measure  the  degree  of  stability  with  which  the  residual 
magnetism  is  held,  and  accordingly  Dr.  Hopkinson  calls  it  the 
"  coercive  force,"  thus  giving  an  exact  and  very  useful  meaning 
to  an  old  loosely  applied  term. 

§  48.  Correction  of  the  foregoing  results  to  allow  for  the 
reaction  of  the  Specimen  on  the  Magnetising  Field. — When 
the  specimen  is  so  long  as  it  was  in  this  instance  (400  diameters), 
its  ends  have  no  great  influence  on  the  field,  and  we  might  with- 
out any  serious  error  ignore  the  difference  between  H'  and  H, 
and  take  the  magnetising  force  of  the  solenoid  to  represent  the 
whole  magnetic  force.  An  approximately  correct  allowance  for 
the  effect  of  the  ends  may,  however,  be  made  by  treating  the 
specimen  as  an  ellipsoid.*  By  §  33  we  have,  in  that  case, 

H  =  H'-  0-00045  I. 

Thus,  for  instance,  the  magnetic  force  producing  a  magnetisa- 
tion of  1,000  is,  on  this  basis,  0'45  units  less  than  the  force  due 
to  the  solenoid,  and  for  other  values  of  I  a  proportional  correc- 
tion is  to  be  made.  We  may  therefore  allow  for  this  in  the 
diagramf  (Fig.  20)  by  drawing  a  straight  line,  0  E,  from  0  to 
cut  the  line  of  I  =  1,000  at  a  force  of  0'45.  Then  the  true  value 
of  H  for  any  point  in  the  curve  of  magnetisation  is  to  be 
measured  from  this  line,  instead  of  from  the  line  0  C.  In  other 
words,  the  effect  of  the  ends  of  the  specimen  is  to  shear  the 
diagram  in  the  direction  in  which  H  is  drawn,  through  the  angle 
C  0  E ;  and  we  may  deduce  the  corrected  curve  from  the  original 
curve  0  A  B  by  setting  each  point,  such  as  A,  back  through  a 
distance,  A  A',  equal  to  the  distance  between  0  E  and  the  axis 
0  C  for  the  corresponding  value  of  I.  The  same  construction 

*  Probably  this  correction  is  rather  excessive.  In  a  cylindrical  rod  the 
magnetism  is  more  nearly  concentrated  at  the  ends  than  in  an  ellipsoid. 
Its  effect  on  the  magnetic  force  is  unequal  at  different  parts  of  the  length, 
but  its  mean  effect  may  be  expected  to  be  less  than  in  the  case  of  an 
ellipsoid. 

f  This  construction  is  used  by  Lord  Rayleigh  in  a  Paper  on  "  The  Energj 
of  Magnetised  Iron"  (Phil.  Mag.,  Vol.  XXII.,  1886,  p.  175). 


RESIDUAL   MAGNETISM   AND   COERCIVE   FORCE. 


55 


obviously  applies  to  the  descending  limb.  The  dotted  curves 
0  A'  B  and  B  C'  D  have  been  drawn  in  this  way,  and  they  may 
be  accepted  as  giving  a  more  nearly  correct  representation  of 
the  relation  of  I  to  H  than  is  given  by  the  original  curves. 

One  effect  of  this  change  is  to  make  the  measured  suscepti- 
bility greater :  its  maximum  value  (which  is  found  by  drawing 
a  tangent  from  0  to  the  curve)  rises  from  189  to  209.  Another 
effect  is  to  increase  the  residual  magnetism,  making  it  93 '8 
per  cent,  of  the  induced  magnetism  instead  of  92'1  per  cent. 
Another  effect  is  to  increase  the  steepness  of  the  gradient  in  the 
steep  part  both  of  the  ascending  and  of  the  descending  limb. 

Table  II.  gives  the  results  of  the  same  experiment  (for  the 
ascending  process)  on  the  above  supposition  that  the  correction  of 
H  to  be  made  on  account  of  the  ends  of  the  specimen  does  not 
sensibly  differ  from  the  correction  which  would  have  to  be  made 
in  an  ellipsoid  400  (equatorial)  diameters  long.  Values  of  B, 
fj,  and  K  are  given  as  well  as  I  and  H.  B,  which  is  4  TT  I  +  H, 
is  so  nearly  equal  to  4  TT  I  that  we  might  adapt  the  curve  of 
Fig.  20  to  exhibit  the  relation  of  B,  instead  of  I,  to  H,  by 
simply  altering  the  scale  of  the  ordinates,  so  that  100  of  I 
should  represent  1257  of  B. 

TABLE  II. 


H 

1 

^ 

B 

^ 

0 

0 



0 

_ 

0-32 

3 

9 

40 

120 

0-84 

13 

15 

170 

200 

1-37 

33 

24 

420 

310 

214 

93 

43 

1,170 

550 

2-67 

295 

110 

3,710 

1,390 

3-24 

581 

179 

7,300 

2,250 

3-89 

793 

204 

9,970 

2,560 

4-50 

926 

206 

11,640 

2,590 

5-17 

1,009 

195 

12,680 

2,450 

6-20 

1,086 

175 

13,640 

2,200 

7-94 

1,155 

145 

14,510 

1,830 

979 

1,192 

122 

14,980 

1,530 

11-57 

1,212 

105 

15,230 

1,320 

15-06 

1,238 

82 

15,570 

1,030 

19-76 

1,255 

64 

15,780 

800 

21-70 

1,262 

58 

15,870 

730 

56  MAGNETISM   IN   IRON. 

§  49.  Differential  Susceptibility  and  Differential  Permeability. 
In  many  cases  we  are  less  concerned  to  know  the  actual  ratio 
of  I  or  of  B  to  H  than  to  know  the  rate  at  which  \  or  B  is 
increasing  or  diminishing  with  respect  to  H — in  other  words, 
the  gradient  of  the  magnetisation  curve.  We  have  seen  that 

the  gradient  — —  begins  by  being  small,  then  becomes  very  large, 
an 

and  then  again  becomes  small  as  the  region  of  saturation  is 
approached.  Prof.  Knott  has  proposed  to  call  this  quantity  the 

"differential  susceptibility";  similarly may  be  called  the 

cm 

differential  permeability.  In  the  example  which  has  been 
quoted,  the  differential  susceptibility  (after  applying  the  ellip- 
soidal correction)  has  a  maximum  value  in  the  ascending  limb 
of  530,  which  is  sensibly  constant,  while  I  changes  from,  say, 
150  to  650.  The  corresponding  differential  permeability  is 
6,660.  In  the  descending  limb  the  greatest  differential  suscep- 
tibility is  1,660,  and  this  is  sensibly  constant,  while  I  changes 
from  700  to  0  (and  to  -  700,  as  we  shall  see  later  in  other 
examples).  The  corresponding  differential  permeability  is 
20,850. 

§  50.  Supplementary  Remarks  on  the  Magnetometric  Method. 
In  testing  the  magnetisation  of  soft  iron,  especially  if  the 
specimen  be  at  all  thick — it  will  be  found  necessary  to  pause 
after  each  increase  in  the  magnetising  current,  and  to  keep  the 
current  constant  for  some  seconds,  or  even  minutes,  before  the 
iron  takes  its  full  magnetisation.  The  "creeping  up"  of  the 
magnetometer  deflection  which  takes  place  after  each  increase 
of  magnetising  force  will  be  spoken  of  more  fully  in  a  later 
chapter. 

If  the  specimen  is  placed  rather  near  the  magnetometer  and 
the  deflection  threatens  to  become  greater  than  the  scale  will 
measure,  the  magnetometer  needle  may  be  brought  back 
towards  its  undeflected  position  by  using  a  permanent  magnet 
(a  hard  steel  wire  will  do  well)  to  counterbalance  a  part  of  the 
deflecting  force  exerted  by  the  specimen  under  examination. 
This  compensating  magnet  must  be  placed  so  that  it  exerts  no 
force  at  the  magnetometer  except  in  the  direction  exactly  oppo- 
site to  that  of  the  force  the  specimen  exerts.  In  other  words, 


SUPPLEMENTARY   REMARKS    ON    MAQNETOM  ETRIO    METHOD.       57 

it  must  exert  deflecting  force,  not  directing  force  (§  39),  and  to 
secure  this  it  should  be  placed  before  or  behind  the  magneto- 
meter (pointing  towards  it)  in  the  line  B  A  E  of  Fig.  18. 
When  the  compensating  magnet  is  introduced,  the  number  of 
scale  divisions  through  which  it  causes  the  needle  to  return  is 
to  be  noted,  and  this  is  to  be  added  to  subsequent  scale  readings 
in  reckoning  the  virtual  deflection.  The  compensating  magnet 
is  specially  convenient  if  we  wish  to  examine  the  effect  of 
applying  or  removing  a  small  amount  of  magnetic  force  when 
the  specimen  is  already  somewhat  strongly  magnetised. 


Magnetising  Current. 
FIG.  21. 

A  useful  method  of  getting  increased  sensibility  is  to  use  a 
compensating  coil  (§  41)  to  balance  a  part  (or  even  the 
whole)  of  the  deflection  produced  by  the  magnetisation  of  the 
specimen  itself.  Suppose,  for  instance,  that  it  is  desired 
to  examine  particularly  the  form  of  the  magnetisation  curve 
under  moderately  weak  magnetic  forces — say  the  part  0  A  B  of 
the  curve  (Fig.  21) — we  may  set  the  specimen  near  the  magneto- 
meter, and  at  the  same  time  advance  the  compensating  coil  so 
that  it  counterbalances  a  large  part  of  the  deflection.  Thus, 
let  PM  be  the  part  of  the  deflection  balanced  by  the  coil, 
when  the  magnetising  current  is  0  M :  the  whole  virtual  deflec- 
tion is  got  by  adding  this  to  P  A,  which  is  the  observed  deflec- 
tion. For  any  stronger  or  weaker  current  the  part  balanced  is 
represented  by  the  corresponding  ordinate  of  the  straight  line 
0  P  Q.  The  slope  of  this  line  is  found  by  observing  the  deflec- 
tion given  by  the  coil  and  solenoid  when  the  specimen  is  taken 


MAGNETISM    IN   IRON. 

out  and  a  known  current  is  applied.  When  the  specimen  is  put 
in  and  the  process  of  magnetisation  is  gone  through,  the  actual 
deflections  of  the  magnetometer  are,  of  course,  limited  to  the 
(positive  or  negative)  portions  of  the  ordinates  intercepted 
between  the  straight  line  0  Q  and  the  curve.  By  adjusting  the 
position  of  the  coil  so  that  0  Q  is  nowhere  far  from  the  curve  a 
high  degree  of  sensibility  becomes  possible,  for  the  whole  range 
of  the  magnetometer  scale  may  then  be  used  in  exhibiting  the 
differences  PA,  Q  B,  &c.  This  method  should  be  specially 
serviceable  in  dealing  with  ellipsoidal  specimens  of  moderate 
length. 

Valuable  as  the  magnetometric  method  has  proved  in 
Investigations  relating  to  the  effects  of  stress  and  other  features 
in  magnetic  quality,  it  cannot  claim  to  be  well  adapted  for 
absolute  measurements  of  magnetic  permeability.  It  has, 
therefore,  no  place  in  the  commercial  testing  of  iron.  To  give 
specimens  the  form  of  ellipsoids  would  be  out  of  the  question 
in  commercial  testing,  and  even  in  long  cylindrical  rods  the 
magnetisation  is  still  too  far  from  uniform  to  allow  absolute 
determinations  to  be  made  with  the  exactness  which  is  now 
necessary.*  Hence,  in  measurements  of  magnetic  permeability 
electrical  engineers  use  either  the  ballistic  method  or  some 
method  of  comparison  in  which  reference  is  made  to  a  standard 
whose  properties  have  been  determined  by  the  ballistic  method. 


*  See  a  Paper  by  Mr.  C.  G.  Lamb,  "  On  the  Distribution  of  Magnetic 
Induction  in  a  Long  Ir^n  Bar,"  Phil.  Mag.,  September,  1899. 


CHAPTER  III. 


MEASUREMENTS   OF   MAGNETIC   QUALITY:    THE 
BALLISTIC  METHOD. 

§  51.  The  Ballistic  Method — The  ballistic  method,  briefly 
alluded  to  in  §  38,  was  invented  by  Weber,  was  used  by 
Thalen,  Stoletow,  Rowland  and  others,  and  received  its  name 
from  Lord  Kelvin,*  It  determines  any  sudden  change  of 
magnetic  induction  by  measuring  the  quantity  of  electricity 
in  the  transient  current  which  is  induced  in  a  coil  wound  over 
the  magnetised  piece.  Let  a  coil,  which  for  brevity  we  may 
call  the  secondary  coil,  be  wound  on  the  bar  or  ring  or  other 
specimen  which  is  to  be  magnetised.  The  coil  need  not  extend 
over  the  whole  length  of  the  specimen,  and  in  the  case  of  a  bar 
a  short  coil  is  best,  wound  over  the  central  part  only,  where  the 
magnetisation  is  most  nearly  uniform.  The  coil  is  to  be  put  in 
circuit  with  a  galvanometer,  the  needle  of  which  has  a  con- 
siderable moment  of  inertia  (in  relation  to  the  directive  force 
acting  on  it),  so  that  it  swings  slowly.  An  ordinary  mirror 
galvanometer  is  easily  adapted  to  serve  as  a  ballistic  galvano- 
meter by  fixing  a  small  weight  to  the  mirror.  If  the  speci- 
men is  wound  with  a  magnetising  solenoid  sudden  changes 
of  its  magnetism  may  be  produced  by  applying  a  magnetising 
current,  by  increasing  it  by  steps,  by  reversing  it,  and  so  on ; 
and  each  of  these  will  cause  a  "  throw,"  or  impulsive  deflec- 
tion of  the  ballistic  needle,  which  will  be  proportional  to  the 
whole  change  of  magnetic  induction  within  the  secondary  coil. 
The  "throw"  is  proportional  to  the  whole  quantity  of  elec- 
tricity which  passes  in  the  transient  current,  and  this  in  its  turn 
is  proportional  to  the  change  of  magnetic  induction  within  the 

*  Phil.  Trans.,  Vol.  CLXVL,  p.  693. 


60  MAGNETISM    IN   IRON. 

coil.  Let  Q  be  the  total  number  of  lines  of  magnetic  induction 
within  the  secondary  coil,  and  A  Q  any  sudden  change  which 
this  number  undergoes.  Let  N2  be  the  number  of  turns  in  the 
secondary  coil,  and  R2  the  whole  resistance  of  the  secondary 
circuit  (in  ohms),  including,  of  course,  the  resistance  t<f  the 
ballistic  galvanometer.  Then  the  whole  quantity  of  electi'city 
in  the  corresponding  transient  current  is 

N2AQ 


The  observed  throw  of  the  galvanometer  measures  this,  and 
the  simplest  way  to  calculate  A  Q  from  it  is  to  compare  this 
throw  with  that  which  occurs  when  the  number  of  lines  of 
induction  within  a  coil  in  the  secondary  circuit  is  changed  by 
a  known  amount.  In  other  words,  we  may  most  conveniently 
standardise  the  ballistic  galvanometer  by  finding  what  throw 
a  known  change  of  induction  causes. 

§  52.  Earth  Coil.  —  Suppose,  for  instance,  that  there  is 
included  in  the  secondary  circuit  another  coil,  consisting  of  a 
number  of  turns  of  wire  wound  on  a  pretty  large  frame,  and 
that  this  is  laid  flat  on  a  horizontal  table,  so  that  it  may  be 
suddenly  turned  over.  By  turning  it  over  we  cause  the  direc- 
tion of  the  vertical  component  of  the  earth's  magnetic  force  in 
it  to  be  reversed,  and  thus  induce  a  throw  of  the  ballistic  gal- 
vanometer due  to  a  known  change  in  the  number  of  lines  of 
induction  within  the  circuit,  from  which  it  is  easy  to  interpret 
the  throws  that  are  produced  by  changes  in  the  magnetism  of 
the  specimen. 

This  "  earth  coil,"  as  it  may  for  brevity  be  called,  was  first 
used  in  magnetic  researches  by  Rowland.*  Instead  of  lying 
horizontally  it  may  stand  vertically,  facing  towards  the  magnetic 
north  and  south,  so  that  when  turned  over  it  will  cut  the  hori- 
zontal component  of  the  terrestrial  field,  or  it  may  be  set  at 
right  angles  to  the  dip,  so  that  the  whole  terrestrial  field  acts 
upon  it.  The  horizontal  or  the  vertical  position  is,  however, 
more  convenient.  For  the  former  a  light  wooden  frame  lying 
on  the  table  answers  well.  Fig.  22  is  engraved  from  a  photo- 

*  Phil  Mag.,  Vol.  XLVI,  1873. 


EARTH   COIL.  61 

graph  of  an  earth  coil,  which  the  writer  has  found  serviceable ; 
the  coil  is  wound  on  a  large  brass  ring  mounted  on  trunnions 
and  furnished  with  projecting  stops,  which  strike  against  the 
post  P  and  allow  the  coil  to  turn  just  180  degrees.  When  the 
post  P  is  standing  up,  as  in  the  figure,  the  coil  lies  horizontally, 
and  the  vertical  component  of  the  earth's  force  is  then  the 
active  field ;  but  the  post  can  fold  down  by  means  of  a  hinge  so 
that  the  coil  stands  vertically,  and  it  may  then  be  set  to  cut 
the  horizontal  component. 

Let  N]_  be  the  number  of  turns  in  the  earth  coil,  Ax  its  area 
in  square  centimetres,  and  F  the  (known)  value  of  that  com- 


Fio.  22.  —  Earth  Coil  for  use  in  Ballistic  Measurements. 

ponent  of  terrestrial  magnetic  field  which  acts  upon  it.  A 
sudden  turning  over  of  the  coil  changes  the  number  of  lines 
within  it  by  the  amount  2  A1  F,  and  the  whole  quantity  of  the 
transient  current  is 


R!  being  the  resistance  of  the  secondary  circuit  at  the  time 
when  the  observation  with  the  earth  coil  is  made.  It  is  con- 
venient and  generally  quite  practicable  to  keep  the  earth  coil 
continuously  in  the  secondary  circuit,  in  which  case  Rj  =  Rj. 
Let  6?x  be  the  ballistic  throw  produced  by  the  earth  coil,  and  let 


62  MAGNETISM   IN    IRON. 

c?2  be  the  throw  produced  by  the  magnetic  change  A  Q,  which 
we  wish  to  evaluate  : 


then, 

from  which  A  Q  = 


§  53.  Use  of  a  Solenoid  and  Current  for  Standardising 
the  Ballistic  Galvanometer.  —  To  use  the  earth  coil  successfully 
we  must  know  with  sufficient  accuracy  the  horizontal  or  the 
vertical  component  of  the  local  magnetic  field.  These  are  apt 
to  vary  in  a  rather  capricious  way  within  a  magnetic  laboratory. 
The  following  method  of  standardising  a  ballistic  galvanometer 
(due,  the  writer  believes,  to  Sir  William  Thomson)  is  a  good 
substitute  for  the  method  of  the  earth  coil.  The  results  it 
gives  are  independent  of  variation  in  the  local  field,  but  depend 
on  the  absolute  measurement  of  a  current.  A  long  magnetising 
coil  is  to  be  uniformly  wound  on  a  brass  tube  or  a  wooden  rod, 
or  some  other  non-magnetic  core,  the  diameter  of  which  must  be 
accurately  known.  Over  this  primary,  at  the  middle  of  its 
length,  a  short  secondary  coil  is  to  be  wound,  and  put  in  circuit 
with  the  ballistic  galvanometer.  Let  A3  be  the  mean  area  of  the 
primary  coil,  and?i3  the  number  of  turns  in  it  per  centimetre  of 
the  length.  Then,  if  a  current,  0  (C.-G.-S.  units),  be  made  to 
pass  through  it,  the  magnetic  force  (or  induction)  within  it  (at 
any  place  near  the  middle)  is  4  TT  C  nB  per  square  centimetre, 
and  the  whole  number  of  lines  of  force  (or  induction) 
which  the  current  introduces  within  the  coil  is  4  TT  C  n%  A3. 
If  N4  is  the  whole  number  of  turns  in  the  secondary  coil,  and 
R4  the  resistance  of  its  circuit,  the  quantity  of  electricity  in  the 
transient  current  that  passes  when  the  primary  current  C  is 
made  or  broken  is 


Let  e/4  be  the  throw  which  this  produces,  then 
4 


CALIBRATING    THE   BALLISTIC    GALVANOMETER.  63 

Still  another  way  of  standardising  the  ballistic  galvanometer 
is  to  discharge  through  it  a  known  quantity  of  electricity, 
namely  from  a  condenser  of  known  capacity,  charged  to  a 
known  potential.  This  has  no  particular  advantage  over  the 
methods  already  described,  and  it  is  less  likely  to  be  accurate 
in  practice. 

§  54.  Damping  and  Calibration  of  the  Ballistic  Gal- 
vanometer.— In  some  uses  of  the  ballistic  galvanometer  it  is 
important  that  there  should  be  little  "damping" — in  other 
words,  that  the  swinging  of  the  needle  should  subside  very 
slowly.  But  in  magnetic  observations  of  the  kind  now  under 
description — when  what  we  deal  with  is  merely  the  comparison 
of  different  ballistic  effects — this  is  not  necessary :  it  is,  in 
fact,  desirable,  as  a  matter  of  convenience,  to  have  a  good 
deal  of  damping,  provided  always  there  is  not  so  much  as  to 
prevent  the  throws  from  being  proportional  to  the  changes  of 
magnetic  induction.  To  test  whether  this  condition  is  satisfied, 
a  series  of  successive  currents  of  increasing  strength  should  be 
made  and  broken  in  the  primary  coil  of  §  53,  while  the  corre- 
sponding throws  are  observed  and  compared  with  the  strength 
of  the  primary  current,  to  see  that  the  two  vary  together. 
Another  plan  is  to  have  a  small  induction  coil  (in  circuit  with 
the  ballistic  galvanometer)  slipped  upon  a  long  bar  magnet 
Pull  the  coil  quickly  off  the  magnet,  and  observe  the  throw ; 
then  reduce  the  number  of  turns  in  the  coil  by  unwinding  one 
or  more  of  them,  and  observe  the  reduced  throw  when  the  coil 
is  again  pulled  off,  and  so  on,  until  the  number  of  turns  and  the 
throw  is  greatly  reduced.  The  observed  throws  should  be  pro- 
portional to  the  successive  numbers  of  turns  in  the  coil. 

To  save  time  between  ballistic  readings,  it  is  convenient, 
especially  when  the  damping  is  not  very  considerable,  to  follow 
Rowland's  plan  of  including  in  the  secondary  circuit  a  small 
coil  slipped  upon  a  magnet.*  By  pulling  it  off  or  slipping  it 
on  at  the  right  moment,  while  the  needle  is  swinging,  the  observer 
may,  with  a  little  practice,  succeed  in  giving  the  needle  a  check, 
which  brings  it  quickly  to  rest.  Care  must,  of  course,  be  taken 
that  this  coil  is  not  moved  while  observations  are  being  made. 

*  Phil.  Mag.,  Vol.  XL VI.,  1873,  p.  147. 


64 


MAGNETISM    IN    IRON. 


§  55.  Ballistic  Tests  of  Kings  and  Rods. — Fig.  23  illustrates 
the  ballistic  method  as  applied  to  a  magnetic  ring.  The  ring  A 
is  wound  all  over  with  a  primary  or  magnetising  solenoid,  the 
current  in  which  is  measured  by  GI}  and  can  be  subjected  to 
sudden  variations  by  putting  in  or  drawing  out  the  plugs  of 
the  resistance-box  B1}  or  can  be  made,  broken,  or  reversed  by 
the  key  K.  G2  is  the  ballistic  galvanometer,  in  circuit  with  a 
secondary  or  induction  coil  (wound  over  a  part  or  the  whole  of 
the  ring),  with  the  resistance  box  B2,  by  which  the  amount  of 
the  throws  may  be  varied,  the  earth  coil  E  and  the  small  coil  D 


e.  "lUH 

FIG.  23. — Diagram  of  Connections  for  Ballistic  Method. 

which  is  used  to  check  the  swinging  of  the  needle.  In  addition 
to  the  parts  shown,  it  is  convenient  to  include  in  the  primary 
circuit  the  arrangement  of  liquid  slide  and  rapid  reversing  key 
for  demagnetising  by  reversals,  as  explained  in  §  42.  By  this 
means  we  can  ensure  that  the  ring  is  in  a  magnetically  neutral 
state  to  begin  with. 

To  test  the  permeability  and  to  determine  the  form  of  the 
magnetisation  curve,  one  or  other  of  two  plans  may  be  followed  : 
(1)  By  Steps.  A  weak  current  may  be  applied  and  the  throw 
noted,  then  the  resistance  at  B2  may  be  suddenly  reduced,  and 


BALLISTIC   TESTS    OF   RINGS    AND    RODS.  05 

the  additional  throw  noted,  and  so  on,  each  throw  measuring 
the  magnetic  effect  of  a  sudden  increase  in  the  magnetising 
current.  The  whole  magnetism  acquired  at  any  stage  is  then 
to  be  estimated  by  summing  up  the  throws.  The  same  process 
evidently  allows  us  to  trace  the  individual  and  cumulative 
effects  of  successive  diminutions  in  the  strength  of  the  magnetis- 
ing current,  and  thus  to  trace  the  magnetisation  curve  through- 
out any  step-by-step  process  of  applying,  removing,  or  reversing 
magnetising  force.  This  is  its  advantage  :  on  the  other  hand, 
it  has  the  practical  drawback  that  if  an  error  happen  to  be  made 
in  measuring  the  throw  at  any  step  it  is  carried  forward  and 
affects  all  the  subsequent  values  of  the  magnetisation.  (2)  By 
Reversals.  Another  plan  is  to  suddenly  reverse  the  current  in 
the  primary  coil.  Half  the  throw  is  then  taken  as  measuring 
the  actual  magnetisation.  Breaking  the  current  also  allows 
the  permanent  magnetism  to  be  calculated  by  showing  the 
amount  that  disappears  in  the  withdrawal  of  the  magnetic  force. 
As  to  the  effect  of  each  reversal,  care  must  be  taken  that  the 
currents  are  progressively  increased,  and  even  then  the  assump- 
tion that  half  of  that  effect  measures  the  total  magnetism  is 
not  quite  accurate,  especially  in  the  case  of  hard  iron  or  steel, 
which  is  less  ready  to  be  magnetised  by  a  force  of  one  sign 
after  a  force  of  the  opposite  sign  has  been  applied  than  if 
the  opposite  force  had  not  acted.  In  soft  iron  the  curve  of 
magnetisation  as  determined  by  this  process  of  reversals  is  not 
materially  different  from  the  curve  determined  by  the  process 
of  steps. 

In  applying  the  ballistic  method  to  long  rods  or  ellipsoids,  or 
other  specimens  with  ends,  either  of  these  processes  may,  of 
course,  be  used,  and  in  addition  a  third  plan  is  practicable — 
namely,  to  have  the  secondary  coil  arranged  so  that  it  may 
be  suddenly  slipped  off  the  magnetised  piece.  The  effect  of 
slipping  it  off  is  to  reduce  the  lines  of  induction  within  it  to 
zero,  provided  the  coil  be  at  once  drawn  far  enough  away  to 
get  practically  out  of  the  magnetic  field,  and  the  throw  of 
the  galvanometer  therefore  measures  the  whole  magnetisation 
which  existed  just  before  the  coil  was  removed.  This  method 
is  often  useful,  but  it  must  be  borne  in  mind  that  the  me- 
ehanical  disturbances  caused  by  pulling  off  the  coil  may, 
especially  with  soft  iron,  alter  very  seriously  the  amount  of 

9 


66  MAGNETISM    IN    IRON. 

magnetism  associated  with  any  assigned  value  of  the  magnetic 
force.  This  will  be  evident  later  when  reference  is  made  to  the 
effects  of  vibration  on  the  magnetic  susceptibility  of  iron.  We 
cannot,  therefore,  use  this  plan  to  trace  the  effects  of  successive 
currents  of  ascending  and  descending  strength.  After  the  step- 
by-step  process,  however,  has  been  applied  to  a  long  rod, 
slipping  off  the  coil  affords  a  useful  test  of  the  accuracy  with 
which  the  summation  of  the  steps  has  been  carried  out. 

§  56.  Calculation  of  B  from  Ballistic  Measurements.— 
We  have  seen  how  the  ballistic  measurements  serve  to  determine 
Q,  the  whole  number  of  lines  of  induction  within  the  secondary 
coil.  If  the  secondary  coil  is  wound  close  upon  the  iron,  very 
nearly  the  whole  of  these  lines  lie  within  the  iron,  and  we  then 

have  B  =  — ,  where  S  is  the  area  of  cross-section  of  the  iron  in 
S 

square  centimetres.  If,  however,  the  area  of  the  secondary 
coil  includes  any  sensible  air  space  (or  other  non-magnetic 
space)  in  addition  to  the  iron,  a  suitable  deduction  must  be 
made  from  Q  before  dividing  by  the  area  of  cross- section  of  the 
iron  to  find  B.  Thus  if  the  secondary  coil  is  outside  the 
primary,  and  the  mean  area  of  the  primary  coil  is  S',  we  shall 
have  (S'  -  S)  H  lines  enclosed  within  the  secondary  coil,  but 
outside  of  the  iron,  and  this  number  will  fall  to  be  subtracted 
from  Q.  Even  when  the  secondary  coil  is  wound  directly  upon 
the  iron,  its  mean  area  is  necessarily  somewhat  greater  than 
the  section  of  the  core,  and  there  is  consequently  a  small 
correction  to  be  applied  (namely,  the  difference  of  these  areas 
multiplied  by  H),  but  the  amount  of  this  correction  is  generally 
insignificant. 

§  57.  Magnetic  Force  in  Rings. — Though  the  magnetising 
solenoid  be  uniformly  wound  over  the  whole  ring,  so  that  its 
effect  at  any  one  cross-section  is  the  same  as  at  any  other, 
the  magnetic  force  is  not  quite  uniform  throughout.  It  is 
strongest  at  the  inner  side — the  shortest  length — of  the  ring, 
and  decreases  towards  the  outer  side  in  proportion  as  the 
radius  of  the  ring  increases.  This  is  because  the  number  of 
turns  per  centimetre  is  greatest  at  the  inner  side  and  least  at 
the  outer.  Let  N  be  the  whole  number  of  turns  of  the  mag- 


MAGNETIC   FORCE   IN   RINGS.  67 

netising  solenoid,  the  number  per  centimetre  at  any  radius  r  is 


N     and  the  magnetic  force  is  47rGN,  or  Thus  the 

2irr  27T7*  r 

2  C1  N  SON" 

magnetic  force  varies  from  -   at  the  inside  to  —  !—  at  the 

rl  r2 

outside  (Fig.  24).  So  far  as  it  goes,  this  is  a  drawback  to 
ihe  use  of  ring-shaped  specimens. 

To  prevent  this  objection  from  having  much  weight  the 
thickness  of  the  ring  should  be  small  compared  with  its  radius. 
The  form  shown  in  Fig.  25  allows  a  small  ring  to  be  used  with- 
out excessive  variation  of  magnetic  force  over  the  section,  and 
without  unduly  reducing  the  sectional  area. 

In  dealing  with  weak  magnetic  forces  it  is  desirable  to  place 
the  ring  in  such  a  position  that  the  earth's  magnetic  field  does 
not  affect  the  uniformity  of  its  magnetisation,  namely,  in  the 

I  r 


FIG.  24.  Fio.  25. 

plane  perpendicular  to  the  direction  of  the  lines  of  terrestrial 
force.  For  the  sake  of  homogeneity  in  the  metal  itself,  a  ring 
turned  out  of  a  solid  block  is  to  be  preferred  to  one  that  is 
forged  from  a  bar. 

§  58.  Bar  and  Yoke. — The  condition  of  endlessness,  which  is 
realised  perfectly  in  a  ring  of  uniform  section,  uniformly  wound 
(or,  rather,  is  realised  as  perfectly  as  the  imperfect  homo- 
geneity of  the  metal  will  allow),  can  be  approximated  to,  even 
when  the  sample  has  the  form  of  a  short  bar,  by  a  very  inte- 
resting and  useful  method,  invented  by  Hopkinson.*  Let 
the  ends  of  the  bar  be  sunk  in  holes  in  a  massive  yoke 
(Fig.  26)  which  has  an  area  of  cross-section  many  times  greater 
than  that  of  the  bar,  and  is  made  of  the  most  permeable 

*  "  Magnetisation  of  Iron,"  Phil.  Trans.,  1885,  p.  455. 

F9 


gg  MAGNETISM    IN    IRON. 

material  available,  namely,  soft  annealed  wrought  iron.  The 
yoke  is  so  much  better  a  conductor  of  lines  of  magnetic  in- 
duction that  the  lines  which  proceed  from  either  end  of  the 
bar  nearly  all  pass  back  through  it  to  the  other  end,  instead  of 
escaping  into  surrounding  space.  This  closing  of  the  magnetic 
circuit  through  the  yoke  prevents  the  bar  from  exercising 
almost  any  self-demagnetising  force  upon  itself ;  and  if  the 
bar  is  wound  with  a  magnetising  solenoid  throughout  its 
whole  clear  length  within  the  yoke,*  the  magnetic  force 
actually  operative  on  it  is  only  a  very  little  less  than  the  whole 
force  due  to  the  solenoid. 

The  amount  of  the  difference  will  be  more  easily  discussed 
when  we  come,  later,  to  speak  of  the  magnetic  circuit  as  a 


FIG.  26. — Yoke  for  the  Ballistic  Tests  of  Bars. 

whole,  and  the  relation  of  the  induction  in  it  to  the  whole 
number  of  ampere-turns  in  the  magnetising  coil.  Meanwhile, 
it  may  suffice  to  say  that  the  magnetism  of  the  bar  and  yoke 
reacts  to  a  small  extent  on  the  magnetic  force,  reducing  it  by 
amounts  which  are  proportional,  or  nearly  so,  to  the  magnetisa- 
tion. The  effect  is  like  that  which  has  already  been  described 
ats  occurring  in  a  long  rod  or  long  ellipsoid,  not  so  extremely 
long  as  to  be  virtually  endless,  and  the  curve  of  magnetisation 
is  consequently  sheared  over  (§  48) :  the  apparent  susceptibility 
and  the  residual  magnetism  are  reduced.  This  makes  the 
method  of  the  yoke  unsuitable  for  accurate  determination  of 
the  susceptibility  and  retentiveness  of  a  very  susceptible  metal, 

*  In  the  figure  the  bar  is  shown  in  its  place,  but  the  magnetising  sole- 
noid and  the  induction  coil  are  omitted. 


BAR   AND    YOKE. 


69 


like  soft  wrought  iron ;  but  there  is  no  serious  error  in  the 
case  of  hard  iron  or  steel. 

The  ends  of  the  bar  should  be  sunk  for  a  considerable  dis- 
tance into  the  yoke,  and  should  fit  in  the  holes  without  shake, 
or  if  there  is  any  appreciable  clearance  its  effect  in  producing 
If-demagnetising  force  may  be  considerable. 

§  59.  Hopkinson's  Application  of  the  Bar  and  Yoke. — In 

applying  the  ballistic  method  to  a  bar  in  a  yoke  we  may,  of  course, 
proceed  by  steps  or  by  reversals,  as  with  a  ring.  In  Hopkinson's 
original  use  of  the  yoke,  however,  a  different  procedure  was 
followed.  The  bar  was  made  in  two  parts,  C  and  C'  (Fig.  27), 
which  abutted  against  one  another  near  the  middle,  where  the 


FIG.  27. 


secondary  coil  D  was  slipped  on,  in  a  space  between  two  halves 
of  the  magnetising  solenoid  B  B.  A  clutch  fixed  on  the  pro- 
jecting end  of  the  rod  G  enabled  it  to  be  suddenly  drawn  away 
from  C'  sufficiently  to  allow  D  (which  was  pulled  sideways 
by  a  spring)  to  leap  out  of  the  field.  This  gave  a  ballistic  throw 
which  measured  the  actual  magnetic  state  of  the  bar  at  the 
moment  when  C  was  drawn  out.  The  plane  of  section  between 
C  and  C'  is  a  rather  objectionable  feature  in  this  arrangement; 
for,  as  will  be  shown  later,  its  influence  on  the  general  per- 
meability of  the  bar  is  by  no  means  immaterial,  even  when  the 
abutting  surfaces  are  accurately  faced. 

§  60.  Double  Bars  and  Yokes.— Fig.  28  illustrates  an 
arrangement  which  will  serve  well  when  two  equal  bars  of 
the  material  to  be  tested  are  available.  The  bars  should  be  of 


70 


MAGNETISM   IN    IRON. 


considerable  length — twenty  or  more  times  the  diameter,  and 
the  yokes  should  be  short  and  thick.  Equal  magnetising 
solenoids  are  wound  over  the  two  bars,  and  are  connected 
to  give  opposite  directions  of  magnetisation.  The  secondary 
coil  is  preferably  distributed  over  the  middle  region  of  both 
bars.  If  it  is  wished  to  measure  the  actual  magnetic  state  at 
any  time,  one  of  the  yokes  may  be  arranged  so  that  on  pulling 
it  away  it  brings  the  secondary  coils  with  it.  We  shall  revert 
to  this  arrangement  of  two  bars  with  end  yokes  in  the  Chapter 
dealing  with  "  Practical  Magnetic  Testing." 


FIG.  28. 


§  61.  Example  of  the  Ballistic  Method. — In  the  following 
example*  the  specimen  was  a  ring  welded  out  of  a  piece  of 
moderately  soft  annealed  iron  wire  : — 

Diameter  of  wire  forming  the  ring 0'248  cms. 

Area  of  section  of  iron =  0'0483  sq.  cms. 

Mean  radius  of  ring  5  'Ocms.     Mean  circumference  31  -4cms. 
Number  of  turns  in  magnetising  coil...     474 

Number  of  turns  in  secondary  coil 167 

Area  of  earth-coil 1216  sq.  cms. 

Number  of  turns  in  earth-coil 10 

Earth's  force,  cut  by  earth-coil 0'34 

Ballistic  throw  on  turning  over  earth- 
coil    42'9  scale  divisions. 

The  mean  value  of  the  magnetic  force  per  ampere  was, 
therefore : — 


47TX474 


or 


2x474 


10x31-4         10x5-0 


18-96. 


The  resistance  of  the  secondary  circuit  was  not  altered 
throughout  the  experiment,  and  the  correction  for  air-space 
within  the  secondary  coil  was  negligible.  Hence,  from  the 
above  data,  the  change  of  the  induction  B  per  square  cm.  in 


*  From  a  Paper  by  the  Author,  PhiL  Trans.,  1885,  pp.  530-532. 


EXAMPLE    OF    THE   BALLISTIC    METHOD. 


71 


the  iron  corresponding  to  one  scale  division  of  ballistic  throw 
was — 


1216x10x0-34x2 
0-0483x167x42-9 


23-89. 


The  experiment  consisted  in  applying  first  a  weak  magnetic 
force,  and  increasing  it  by  a  series  of  sudden  steps  to  9-14 
C.-G.-S.  units,  and  then  removing  and  finally  re-applying  the 
same  force,  all  by  steps,  while  the  ballistic  throws  were  observed. 
The  following  Table  (III.)  gives  the  results,  /A,  I,  and  K  having 
been  calculated  from  B  and  H. 


TABLE  III. — ANNEALED  WROUGHT-!RON  RINO. 


H. 

Ballistic 
Throw. 

Sum  of 
Throws. 

B. 

/*' 

!. 

K. 

0-13 

1-1 

1*1 

26 

2 

0-26 

1-1 

22 

53 

... 

4 

... 

0-30 

0-5 

2-7 

65 

... 

5 

... 

0-40 

0-8 

3-5 

84 

.  .. 

7 

... 

0-53 

1-0 

4-5 

107 

,  .. 

0 

... 

0-71 

21 

6-6 

158 

... 

12 

... 

0-93 

2-9 

9-5 

227 

... 

18 

... 

1-31 

3-9 

13-4 

320 

245 

25 

19 

1-69 

9-2 

22-6 

540 

320 

43 

25 

1-89 

6-9 

29-5 

705 

370 

56 

30 

2-78 

77-5 

107'0 

2,560 

920 

203 

73 

3-36 

787 

185-7 

4,440 

1,320 

353 

105 

4-01 

82 

2677 

6,400 

1,600 

509 

127 

4-95 

91-5 

359-2 

8,580 

1,740 

683 

138 

5-86 

57 

416-2 

9,940 

1,700 

791 

135 

7-20 

57 

473-2 

11,300 

1,570 

899 

125 

8-10 

23-5 

496-7 

11,870 

1,460 

944 

116 

914 

24 

5207 

12,440 

1,360 

989 

108 

7'83 

-   4-4 

516-3 

12,330 

981 

6-21 

-  6-7 

5096 

12,170 

»•• 

968 

... 

4-75 

-  71 

502-5 

12,000 

.  .. 

955 

... 

2-70 

-14-0 

488-5 

11,670 

.  .. 

929 

... 

0 

-33-2 

455-3 

10,880 

... 

866 

... 

2-78 

15 

470-3 

11,240 

... 

894 

... 

4-95 

14-2 

484-5 

11,570 

... 

921 

... 

6-21 

119 

496-4 

11,860 

.  .. 

943 

... 

8-00 

145 

510-9 

12,170 

... 

971 

... 

9-14 

10 

520-9 

12,440 

... 

990 

... 

72 


MAUJSETISM    IN    IRON. 


The   relation   of    B  to   H  in  this  experiment  is  shown  in 
Fig.  29.     It  will  be  seen  that  the  curve  of  magnetisation  pre- 


12000 
no 

10000 
9000 
8000 
•?ooo 

6000 
5000 
4000 
3000 
2000 
(000 


CD 


7 


*       Magnetic    Force6H 
FIG.  29.  —Wrought- Iron  Ring. 

sents  the  same  characteristics  as  in  the  former  example.     The 
residual  value  of  B  is  88  per  cent,  of  the  induced  value. 

Further  details  of  the  Ballistic  method  will  be  found  in  the 
Chapter  which  deals  with  "  Practical  Magnetic  Testing." 


CHAPTER  IV. 


EXAMPLES  OF  MAGNETISATION. 

§  62.  Ballistic  Method  using  Reversals :  Magnetisation  of 
an  Iron  Ring  (Rowland). — A  few  more  examples  may  be  quoted 
in  further  illustration  of  the  relation  of  magnetisation  to  mag- 
netising force  in  iron. 

In  the  following  experiment  by  Kowland*  the  specimen  was  a 
welded  and  annealed  ring  of  "  Burden's  Best "  wrought  iron, 
6'77cm.  in  mean  diameter  and  0'916  sq.  cm.  in  section.  B  was 
measured  by  reversing  the  magnetising  current  and  taking 
half  the  ballistic  effect.  The  ballistic  effect  of  breaking  the 
magnetising  current  was  also  noted.  This,  subtracted  from  half 
the  effect  of  reversal,  gave  the  residual  magnetism  at  each  stage 
in  the  magnetising  process.  The  results,  reduced  to  C.-G.-S. 
units,  are  given  in  Table  IV.,f  where  the  residual  values  of 
the  magnetic  induction  appear  in  the  third  column  under  the 
heading  Br. 

*  Phil.  Mag.,  Vol.  XLVL,  1873,  p.  151. 

t  The  dimensions  of  H  and  of  B  and  of  I  are (Mass) ^    Kowland, 

(Length)'  (Time) 

in  the  paper  cited,  uses  meZre-gramme-second  units  in  expressing  the  induc- 
tion. His  numbers  (called  Q  in  the  Paper)  have  therefore  to  be  divided  by 
10  to  bring  them  to  C.-G.-S.  units.  With  regard  to  H,  he  gives  (under  the 
heading  M)  numbers  which  are  equal  to  the  magnetic  force  divided  by  ATT. 

These  have  accordingly  to  be  multiplied  by  — ^  to  reduce  them  to  C.-G.-S. 
units  of  H. 


74  MAGNETISM   IN   IRON. 

TABLE  IV.— ANNEALED  WROUGHT-!RON  RING. 


H 

B 

Br 

V- 

•18 

71 

18 

390 

•69 

600 

211 

869 

•86 

967 

439 

1,129 

1-27 

2,460 

1,570 

1,936 

1-41 

2,920 

1,940 

2,078 

1-45 

3,080 

2,060 

2,124 

2-04 

4,960 

3,630 

2,433 

2-22 

5,480 

3,810 

2,470 

2-34 

5,780 

4,010 

2,472 

2-72 

6,650 

4,750 

2,448 

3-16 

7,470 

5,430 

2,367 

4-05 

8,940 

6,270 

2,208 

5-31 

10,080 

6,840 

1,899 

8-48 

12,270 

7,500 

1,448 

10-23 

12,970 

7,670 

1,269 

11-99 

13,630 

7,520 

1,137 

17-69 

14,540 

7,990 

824 

3417 

15,770 

8,130 

462 

46-02 

16,270 

7,850 

354 

64-33 

16,600 

7,890 

258 

Fig.  30  shows  these  values  of  B  and  Br  in  relation  to  H, 
for  forces  up  to  10  C.-G.-S.  Beyond  that  force,  the  residual 
magnetism  becomes  very  nearly  constant.  The  proportion  of 
residual  to  induced  magnetism  is  considerably  smaller  here 
than  in  experiments  with  long  wires  or  with  wires  welded  into 
rings.  Probably  this  is  due  less  to  any  specific  difference 
in  the  material  than  to  a  difference  in  the  conditions  of  the 
experiment.  It  was  shown  long  ago  by  Von  Waltenhofen  that 
when  magnetic  force  is  suddenly  removed  from  an  iron  rod  it 
leaves  less  residual  magnetism  than  when  gradually  removed.* 
This  is  notably  the  case  when  the  specimen  is  comparatively 
thick.  In  a  thick  rod  or  ring  the  sudden  withdrawal  of  mag- 
netic force  sets  up  oscillating  circumferential  currents  in  the 
substance  of  the  metal,  which  have  an  effect  not  unlike  that 
which  is  produced  in  the  process  of  "  demagnetising  by  re- 
versals" (§  42).  With  very  long  wires  or  rings  of  small  section 
one  commonly  finds  80  or  90  per  cent,  of  the  induced  mag- 


*  Pogg.  Ann.,  CXX.,  1863.     See  also  Wiedemann's  Elcktricitat,  Vol.  IV. 


MAGNETISATION   OP  AN   IRON   RING. 


75 


netism  survive  the  removal  of  magnetising  force,  especially 
when  the  force  is  reduced  by  small  steps  or  quite  continuously. 
In  the  present  case  the  force  was  removed  suddenly,  and  the 
ring  was  thick. 


13000 
12000 

1 1000 
10000 
9000 
8000 
7000 
6000 
5000 
4000 
3000 
2000 
1000 


7 


7 


334  567 

Magnehsing    Force  H. 
Fia.  30. — Wrought-Iron  Ring  (Rowland). 


§  63.  Cyclic  Process  of  Magnetisation  :  Long  Iron  Wire. — 
In  this  instance  the  specimen — a  straight  wire  of  very  soft 
annealed  iron,  0-158  cms.  in  diameter  and  64  cms.,  or  400  dia- 


76 


MAGNETISM   IN    IRON. 


meters,  long — was  tested  by  the  step-by-step  ballistic  method,* 
the  magnetic  force  being  first  raised  from  zero  to  17-26 
units,  then  reversed  to  - 17 '26,  then  reversed  again  to 
+ 17 '26,  then  reduced  to  zero,  and  finally  restored  to  +  17-26. 
The  effects  of  these  cyclic  processes  are  exhibited  in  Fig.  31 
sufficiently  to  make  it  unnecessary  to  quote  the  numerical 
values  of  B  and  H.  At  the  beginning  the  wire  had  a  small 


1    2    3    4    5    6    7    8   9  10  11 12  13  14  15  16  17 


17  16  15  14  13  12  11  10  9    8    7    6    54    32    1 

FIG.  31.— Soft  Iron  Wire  (length  =  400  diameters). 

amount  of  initial  magnetism,  which  was  found  by  slipping  off 
the  secondary  coil. 

In  this  figure  tbe  magnetising  force  of  the  solenoid  is 
accepted  as  the  whole  magnetic  force  H,  no  allowance  having 
been  made  for  the  influence  of  the  ends.  If  we  treat  the  rod 

*  From  a  Paper  by  the  Author,  Phil.  Trans.,  1885,  p.  539. 


MAGNETISATION    OF   IRON    RODS.  77 

as  equivalent  to  an  ellipsoid  400  diameters  long,  H  is  to  be 
measured  from  the  line  0  A  instead  of  from  0  Y.* 

On  both  sides  of  the  figure  the  residual  magnetism  is  82  per 
cent,  of  the  induced,  and  the  reversed  magnetic  force  required 
to  remove  it — the  "  Coercive  Force,"  §  47 — is  1-9.  This  figure 
is  thoroughly  typical  of  the  behaviour  of  soft  wrought  iron 
when  subjected  to  cyclic  reversals  of  magnetic  force. 

§  64.  Magnetisation  of  Iron  Rods  of  Various  Lengths.-— 
The  curves  of  Fig.  32  are  selected  from  a  group  of  experi- 
ments! in  which  an  annealed  wire  of  soft  wrought  iron,  origin- 
ally 300  diameters  long,  was  tested  by  the  ballistic  method, 
first  in  its  full  length  and  then  after  the  length  had  been 
reduced  successively  to  200,  150,  100,  75,  and  50  diameters  by 
cutting  off  equal  portions  (in  each  case)  from  the  ends.  The  cen- 
tral part  of  the  length,  through  which  the  magnetic  induction 
was  measured,  remained  unchanged  throughout  the  series. 
After  each  magnetisation  the  rod  was  reduced  to  a  neutral 
state  not  by  the  process  of  reversals,  but  by  taking  advan- 
tage  of  the  fact  that  a  soft  iron  wire  loses  sensibly  the 
whole  of  its  residual  magnetism  when  it  is  briskly  tapped. 
Soft  iron  is  extraordinarily  sensitive  to  the  effect  of  vibration  ; 
to  tap  it  when  the  magnetic  force  is  in  action  increases 
the  permeability  very  greatly,  and  to  tap  it  when  the  force  is 
removed  does  away  almost  completely  with  its  retentiveness. 
So  sensitive  is  it  that  when  the  magnetic  force  is  removed  the 
lightest  touch  of  the  fingers  suffices  to  destroy  much  of  the 
residue,  and  after  brisk  tapping  only  one  or  two  per  cent,  will 
in  some  cases  be  found  to  remain.  The  residual  magnetism  of 
soft  iron  is  in  fact  very  insecurely  held.  So  long  as  the  metal 
is  left  perfectly  at  rest  it  does  not  appear  to  suffer  loss  through 
the  mere  lapse  of  time ;  but  any  variation  of  temperature,  or 
mechanical  disturbance  of  whatever  kind,  reduces  it  with 
remarkable  rapidity. 

*  By  the  table  in  §  33,  the  value  of  ^  for  an  ellipsoid  400  diameters 

long  is  0'000037.  Hence  the  line  0  A  is  drawn  at  such  an  inclination  as  to 
make  the  reaction  of  the  magnetism  upon  the  field  equal  to  a  force  of 
0-37  when  B  is  10,000. 

f  Ewing,  PUt.  Trans.,  1885,  p.  535. 


MAGNETISATION   OF   IRON   RODS.  79 

The  three  curves  selected  for  reproduction  in  Fig.  32  refer 
to  the  cases  where  the  length  was  200,  100,  and  50  times  the 
diameter  respectively.  The  abscissae  give  the  magnetising 
force  exerted  by  the  solenoid,  not  the  true  H,  as  affected  by 
the  ends  of  the  specimen.  To  give  some  idea  of  the  true  H, 
the  lines  0  A,  OB,  and  0  C  have  been  drawn  ;  these  show  the 
reactions  which  ellipsoids  of  200,  100,  and  50  diameters  respec- 
tively would  exert.  By  measuring  the  magnetic  force  from 
them  instead  of  from  0  Y,  we  get  an  approximation  to  the 
true  value  of  H.  The  approximation  is  a  very  fairly  correct 
one  for  the  rods  of  200  and  100  diameters ;  the  curves  for 
them,  when  rectified  by  taking  abscissae  from  0  A  and  0  B 
respectively,  agree  well  with  one  another,  and  with  curves  for 
longer  rods  or  rings  of  the  same  material.  The  diagram  shows 
well  what  has  already  been  sufficiently  explained — how  it  is 
that  soft  iron  shows  little  retentiveness  when  tested  in  the 
form  of  a  short  rod,  though  it  shows  much  when  tested  as  a 
long  rod  or  as  a  ring.  The  broken  lines  show  the  gradual 
reduction  which  the  magnetism  suffered  as  the  magnetising 
force  of  the  solenoid  was  reduced  to  zero.  By  producing  them 
past  the  axis  0  Y  to  cut  0  X  produced  we  find  that  the 
"  coercive  force  "  of  the  material  was  1-9,  as  in  the  experiment 
of  Fig.  31,  §  63,  which  dealt  with  another  specimen  of  the 
same  annealed  iron  wire.* 

§  65.  Wrought-Iron  Bar. — Fig.  33  is  copied  from  a  Paper  by 
Hopkinson,f  and  refers  to  a  ballistic  test  of  annealed  wrought 
iron  by  the  method  of  the  yoke  (§  59).  The  magnetic  force  was 
raised  to  240,  then  reversed  and  re-reversed ;  but  in  the  figure 
the  negative  magnetisation  and  the  parts  relating  to  high  forces 
are  omitted.  A  comparison  of  this  figure  with  those  that  have 
been  already  given  suggests  that  the  condition  of  endlessness 
was  imperfectly  realised  (in  great  part,  no  doubt,  through  the 
action  of  the  plane  of  section  referred  to  in  §  59),  and  that 
the  curves  might  be  approximately  rectified  by  measuring  H 

*  In  further  illustration  of  the  effects  of  length  in  the  magnetisation  of 
rods,  see  a  Paper  by  A.  Tanakadate,  Phil.  Mag.,  November,  1888,  where 
experiments  are  described  dealing  with  a  series  of  rods  shorter  than  those 
referred  to  in  the  text.  See  also  C.  G.  Lamb,  Phil.  Mag.,  Sept.,  1889, 

t  Phil.  Trans.,  1885,  plate  XLVH 


80 


MAGNETISM    IN    IRON. 


from  a  line  such  as  0  A  (which  has  been  adaed  in  copying 
the  figure).  This  would  make  the  bar  within  the  yoke  equiva- 
lent as  regards  endlessness  to  a  bar  (with  free  ends)  about  150 
diameters  long.  The  coercive  force  in  this  sample  has  a  value 
almost  identical  with  the  value  found  in  soft  iron  wire,  which 
strengthens  the  view  that  it  is  to  imperfect  endlessness,  rather 
than  to  any  specific  difference  in  the  quality  of  the  iron,  that 
one  is  to  ascribe  the  comparatively  small  retentiveness  of  this 
bar. 


1700  C 


16000 


10         12     .    "         16         18        20        12        £4       26 

Magnetic  Force  H 
Fia.  33. — Wrought-iron  Bar  in  yoke. 

§  66.  Magnetisation  of  Mechanically  Hardened  Iron. — In 
all  the  examples  which  have  been  given  above  the  iron  was 
annealed  or  softened  by  heating  to  redness.  Iron  which  has 
been  mechanically  hardened — by  hammering,  rolling,  wire- 
drawing, or  straining  in  any  way  beyond  the  limit  of  elasticity 
— shows  much  less  permeability  and  susceptibility,  much  less 
residual  magnetism  (when  tested  in  the  form  of  an  endless 
specimen),  and  considerably  more  coercive  force.  Thus  the 
retentiveness  of  hardened  iron,  when  in  the  form  of  a  very 
long  rod  or  a  ring,  is  less  than  that  of  soft  iron ;  but  a  short 
rod  holds  more  residual  magnetism  when  hard  than  when  soft, 
on  account  of  its  greater  coercive  force. 


MAGNETISATION    OF    MECHANICALLY   HARDENED   IRON.          81 

These  differences  combine  to  give  the  curves  of  magnetisa- 


tion of  hardened  iron  a  roundness  of  outline  by  which  they  are 
readily  distinguished  from  those  of  soft  iron. 


82  MAGNETISM    IN    IRON. 

The  altered  characteristics  of  the  curves  are  well  seen  in 
Fig.  34,  which  shows  the  results  of  two  experiments  made  (by 
the  one-pole  magne  tome  trie  method)  on  the  same  piece  of  iron 
wire.*  In  the  first  the  wire  (0'158  cm.  in  diameter  and  60  cms. 
long)  was  annealed,  and  was  subjected  to  a  cyclic  magnetising 
process  between  the  limits  +46  and  -46  of  H.  The  results 
are  shown  by  the  full  lines  of  the  figure.  The  wire  was  then 
demagnetised  by  reversals,  and  was  hardened  by  stretching  it 
through  about  10  per  cent,  of  its  original  length.  After  the 
stretching  weight  had  been  removed,  a  cyclic  process  of  mag- 
netisation was  gone  through,  the  results  of  which  are  shown 
by  the  dotted  lines.  In  this  figure  the  ordinates  are  the  in- 
tensity of  magnetism  I. 

In  the  soft  state,  the  maximum  of  susceptibility  occurs 
early,  at  a  force  of  2'6,  and  its  value  (K)  is  245  ;  the  maximum 
permeability  is  3,080.  In  the  stretched  state  the  maximum 
of  susceptibility  occurs  much  later,  at  a  force  of  about  11,  and 
its  value  is  only  53  :  the  maximum  permeability  is  670. 

In  the  stretched  state  there  is  less  than  half  as  much 
residual  magnetism  as  in  its  soft  state.  But  stretching  has 
increased  the  coercive  force  from  1'7  to  4'5. 

§  67.  Magnetic  Qualities  of  Steel. — Speaking  generally,  the 
curves  of  magnetisation  for  steel  can  be  made  to  resemble 
closely  those  for  iron  by  simply  altering  the  scale  of  H. 
Under  strong  magnetic  forces  the  region  of  saturation  is 
reached  in  steel  with  much  the  same  value  of  I  or  of  B 
as  in  iron ;  but  to  reach  it  requires  the  application  of  a 
stronger  force.  At  every  stage  the  susceptibility  and  permea- 
bility are  less  in  steel  than  in  iron,  and  the  coercive  force  is 
correspondingly  greater. 

The  name  "steel "covers  as  large  a  variety  of  magnetic  qualities 
as  it  does  of  mechanical.  Beyond  those  differences  which  result 
from  difference  in  chemical  composition,  the  range  is  extended 
by  the  effects  of  mechanical  treatment,  and  above  all  by  the 
effects  of  annealing,  hardening  by  quenching,  and  tempering. 
As  a  rule,  steel  which  is  mechanically  soft  or  "mild"  is  mag- 
netically soft — in  other  words,  its  permeability  is  comparatively 


PUl.  Trans.,  1885,  p.  547. 


MAGNETIC    QUALITIES    OP    STEEL.  83 

high,  and  its  coercive  force  is  low ;  and  steel  which  is 
mechanically  hard  is  magnetically  hard.  Thus,  if  we  compare 
samples  differing  in  their  percentage  of  carbon,  we  find,  in 
general,  corresponding  differences  of  magnetic  hardness;  the 
harder  samples — that  is  to  say,  those  with  more  carbon — are 
less  susceptible  and  have  more  coercive  force.  Again,  as  re- 
gards the  effects  of  temper,  specimens  which  have  been  hardened 
by  quenching  from  a  red  heat  are  magnetically  much  harder 
than  specimens  of  the  same  composition  which  have  been 
annealed.* 

Other  constituents  than  carbon  affect  the  magnetic  quality, 
often  very  greatly.  Chromium  and  tungsten  increase  the 
coercive  force  immensely;  and  tungsten,  in  particular,  is  & 
usual  constituent  in  magnet  steel.  In  soft  iron,  as  we  have 
seen,  the  coercive  force  is  about  2,  or  sometimes  even  less.  In 
chrome  steel,  hardened  by  quenching  in  oil,  it  is  40,  and  in 
tungsten  steel  it  may  exceed  50.  f  These  numbers  are  taken 
from  a  Paper  by  Hopkinson,  which  contains  the  most  important 
data  at  present  available  regarding  the  magnetic  qualities  of 
different  steels.  The  value  of  his  results  is  much  enhanced  by 
the  fact  that  a  chemical  analysis  of  each  sample  is  given.  We 
shall  have  occasion  to  recur  to  them  later  :  meanwhile,  it  may 
suffice  to  illustrate  the  magnetisation  of  steel  by  a  pair  of 
examples  taken  from  the  author's  experiments {. 

§  68.  Magnetisation  of  Pianoforte  Steel  Wire. — Figs.  35 
and  36  show  the  results  of  cyclic  processes  of  magnetisation 
(with  positive  and  negative  magnetic  forces  ranging  up  to 
nearly  100)  applied  to  two  pieces  of  the  same  pianoforte  steel 
wire — one  (Fig.  35)  softened  by  annealing ;  the  other  (Fig.  36) 
glass-hardened  by  quenching  in  water  from  a  red  heat.  The 
coercive  force  in  the  latter  is  scarcely  inferior  to  that  of 
tungsten  steel.  The  maximum  permeability  is  only  118;  in 
Fig.  35  it  is  295. 

*  The  influence  which  differences  of  temper  exert  on  magnetic  retentive- 
ness  has  been  exhaustively  examined  by  Barus  and  Strouhal.  Their  results 
are  published  as  a  Bulletin  of  the  U.S.  Geological  Survey,  No.  14,  1885. 

t  Hopkinson,  Phil.  Trans.,  1885,  p.  463. 

£  Phil.  Trans.,  1885,  pp.  546-7. 

02 


64 


MAGNETISM    IN    IRON. 


Fia.  35.— Pianoforte  Steel  Wire,  annealed. 


FlQ.  36,—  Pianoforte  Steel  Wire,  glass-hard. 


OAST   IRON    AND    NON-MAGNETIC    STEE1S. 


85 


§  69.  Cast  Iron. — Cast  iron  reaches  a  somewhat  lower  mag- 
netisation than  wrought  iron  or  steel,  even  under  strong 
forces.  The  intensity,  when  saturated,  is  about  three-quarters 
that  of  wrought  iron.  In  permeability  under  moderate  mag- 
netising forces,  and  in  coercive  force,  it  generally  resembles 
mild  steel.  Fig.  37  (from  Hopkinson)  exhibits  half  of  a  cyclic 
process  of  magnetisation,  for  what  is  probably  an  exceptionally 
soft  specimen  of  grey  cast  iron,  in  which  the  coercive  force  is 
barely  double  that  of  annealed  wrought  iron.  The  specimen 
was  a  short  bar  tested  by  the  method  of  the  yoke  (§  59). 


12000 


20      40       60 


80      100      120       140      160  ISO 

Magnetic  Force  H. 
Fio.  37.— Cast  Iron. 


800    230    340   £60 


§  70.  Non-Magnetic  Steels. — In  certain  alloys  of  iron  there 
is  a  remarkable  absence  of  magnetic  quality.  The  presence 
of  manganese  in  large  quantities  deprives  the  metal  of  nearly 
all  its  susceptibility.  A  notable  instance  occurs  in  the 
"  manganese  steel "  of  Mr.  Hadfield,  which  contains  about 
12  per  cent,  of  manganese  and  1  per  cent,  of  carbon.  The 
permeability  of  this  alloy  is  only  about  1*3  or  1*5,  and  IB 
sensibly  constant  in  strong  and  weak  magnetic  fields.  There 
is  sensibly  no  residual  magnetism,  even  after  a  very  powerful 
•magnetising  force  has  been  applied.  A  still  more  curious 
Case  is  that  of  "nickel  steel."  Hopkinson*  has  found  a 
specimen  containing  25  per  cent,  of  nickel  to  be  practically 
non-magnetic  under  ordinary  conditions  of  temperature,  its 

*  Proc.  Roy.  Soc.,  Dec.  12,  1889  ;  May  1,  1890. 


86 


MAGNETISM    IN    IRON. 


permeability  being  constant  and  equal  to  about  1*4.  Here  we 
Lave  two  materials,  nickel  and  iron,  each  strongly  magnetic, 
becoming  non-magnetic  when  combined.  What  makes  this  alloy 
peculiarly  interesting  is  the  further  fact  that  when  cooled  to  a 
very  low  temperature,  it  becomes  strongly  magnetic,  and  remains 
so  after  the  temperature  is  again  allowed  to  rise  to  ordinary 
atmospheric  values.  The  effects  of  temperature  on  magnetic 
susceptibility  will  form  the  subject  of  a  later  chapter. 

§  71.  Nickel. — Fig.  38  gives  curves  showing  the  cyclic  mag 
netisation  of  a  long  piece  of  nickel  wire  (0*068  cm.  in  diameter, 
and  25 '4  cms.  long)  first  in  the  annealed  state  (full  lines)  and 
next  after  being  hardened  by  stretching  beyond  the  limit  of 
elasticity  (dotted  lines).*  The  curves  give  I,  not  B.  They  show 
that  under  strong  forces  the  magnetisation  reached  by  nickel 
is  greatly  inferior  to  that  reached  by  wrought  or  cast  iron  or 
ordinary  steels.  (The  saturation  value  of  I  in  nickel  is  J  or 
J  the  saturation  value  in  wrought  iron.)  The  following 
numbers  refer  to  the  experiment  of  Fig.  38  when  the  wire  was 
in  the  soft  state  : — 

Annealed  Nickel  Wire. 


H 

1 

K 

0 

22 

4-0 

36 

6-5 

83 

12-8 

8-0 

177 

22-1 

9-5 

223 

23-5 

10-9 

251 

23-0 

12-3 

273 

22-2 

24-6 

325 

13-2 

52-6 

371 

7-1 

79-7 

392 

4-9 

1004 

401 

4-0 

0 

284 

-7-5 

0 

The  last  numbers  in  columns  1  and  2  of  the  table  show  the 
residual  magnetism  and  coercive  force.  The  greatest  suscep- 
tibility (K  =  23-5)  corresponds  to  p  =  283.  In  the  test  with 

*  Ewing  and  Cowan,  Phil.  Trans.,  Vol.  179A,  1888,  p.  327. 


NICKEL. 


hardened  wire  the  maximum  susceptibility   K   was   only  8'3 
(/*=105)  and  the  coercive  force  was  18.     The  curves  for  an- 


nealed and  mechanically  hardened  niosel  differ  in  much  the 
same  way  as  the  corresponding  curves  for  annealed  and 
hardened  iron. 


88 


MAGNETISM    IN    IRON. 


Rowland,*  using  a  ring  of  cast  nickel,  found  a  maximum  sus- 
ceptibility of  17 '6  (permeability  222),  and  reached  a  value  of  I 
equal  to  434  with  a  force  H  of  104. 

§  72.  Cobalt. — Cobalt  has  decidedly  more  capacity  for  mag- 
netisation than  nickel.  Under  the  action  of  a  strong  field  it 
takes  up  about  as  much  magnetism  as  cast  iron ;  it  has,  how- 
ever, comparatively  little  susceptibility  where  the  magnetising 
force  is  weak. 

Fig.  39  exhibits  an  experiment  on  the  cyclic  magnetisation  of 
a  cobalt  rod  (containing  about  2  per  cent,  of  iron),  cast  and 
turned,  and  tested,  within  a  yoke,  in  the  manner  described  in 
§  58,  the  magnetism  at  each  stage  being  determined  by  sum- 
ming the  ballistic  effects  of  successive  steps.  There  was  a  small 
amount  of  initial  magnetism,  not  removed  when  the  experiment 
began.  The  greatest  permeability  was  found  when  the  force 
was  about  25 ;  its  value  is  174,  which  corresponds  to  a  suscepti- 
bility of  13-8.  Rowland,  using  a  cast  cobalt  ring,  found  a 
maximum  susceptibility  of  11 -2. 

The  curves  for  cobalt  have  a  rounded  outline  recalling  those 
for  hardened  iron.  One  effect  of  this  is  that  the  residual  mag- 
netism is  comparatively  small.  The  coercive  force  in  Fig.  39 
is  12. 

§  73.  Curves  of  Permeability  and  Susceptibility. — The  beha- 
viour of  magnetic  metals  during  the  imposition  of  magnetic 
force  is  sometimes  exhibited  graphically  in  other  ways.  Instead 
of  drawing  a  curve  to  show  the  relation  of  B  or  of  I  to 
H,  as  has  been  done  in  the  examples  already  given,  we  may 
draw  a  curve  showing  the  relation  of  K  or  of  /A  to  H.  This 
method  of  representing  the  results  of  experiment  was  used  by 
Stoletow.f  Another,  and  better  plan,  due  to  Rowland,  J  is  to 
represent  /*,  in  relation  to  B,  or  K  in  relation  to  I.  These  may 
be  called  permeability  curves  and  susceptibility  curves  respec- 
tively. The  following  are  a  few  examples  : — 

§  74.  Susceptibility  Curves  for  Wrought-Iron  Wire. — Fig.  40 
shows  two  curves  of  K  and  I  for  the  experiment  described  in 

*  Phil.  Mag.,  November,  1874.          f  Phil.  Mag.,  January,  1873. 
J  Phil.  Mag.,  August,  1873. 


V     OF  THE 

UNIVERSITY 


COBALT. 


89 


NX 


\ 


x 


a 


joipnpu 


u6e  /\j 


\ 


1 


90 


MAGNETISM    IN   IRON. 


§  C6,  where  the  same  piece  of  wrought  iron  was  tested,  first 
in  the  soft  annealed  state,  and  again  after  being  hardened  by 
stretching.  Curves  of  p  and  B  would  have  the  same  form, 
since  in  wrought  iron  JJL  is  almost  exactly  4  TT  K,  and  B  is  almost 
exactly  4  TT  I. 

The   approximate  symmetry  which   a  curve   of    this   type 
exhibits  about  an  inclined  straight  line  through  the  apex  waa 


O       100     200    300      400   500     600      700    80O    900    1000     1100  1200 

Intensify  o?  Magnetisation.  I. 
Fia.  40. — Relation  of  K  to  I  in  Iron  Before  and  After  Stretching. 


noticed  by  Rowland,  and  leC  him  to  devise  an  empirical  formula, 
from  which,  by  extrapolation  beyond  the  limits  of  experiment,  a 
limiting  or  saturating  value  of  B  or  of  I  might  be  deduced. 
It  has,  however,  been  shown  by  other  observers  that  when  the 
magnetic  force  is  sufficiently  raised  the  curves  cease  to  be  even 
approximately  symmetrical ;  the  empirical  formula  then  fails, 
and  it  is  not  possible  by  producing  the  curve  beyond  experi- 


PERMEABILITY    CURVES    FOR   NICKEL. 


91 


mental  values  to  find  a  limiting  intensity  of  magnetisation. 
There  is  a  true  saturation  value  of  I  (not  of  B),  as  will  be  shown 
later;  but  it  cannot  be  found  in  the  manner  suggested  by 
Rowland,  because  the  curve  of  K  and  I  or  of  /x  or  B  bends  out 
under  high  forces,  becoming  concave  on  its  upper  side.  This 
feature  will  be  seen  below  in  the  corresponding  curves  for 
nickel  and  cobalt. 

§  75.  Permeability  Curves  for  Nickel.— Fig.  41  gives  three 
permeability  curves  for  a  nickel   rod  in  the  annealed  state, 


300 


250 


200 


150 


100 


50 


..... 


per 


r.o\ 
lead 


BNkilot 
sqm 


6-8 Mos  pe-sq.mm. 


1000 


2000  3000  4000  5000 

Magnetic  Induction  B 


Fia.  41. — Permeability  of  Nickel  in  the  Annealed  State. 


tested  within  a  yoke : — The  lowest,  shown  by  a  full  line,  is 
the  curve  got  when  the  rod  was  tested  under  ordinary  condi- 
tions; the  other  two,  shown  by  dotted  lines,  relate  to  tests  made 
when  the  rod  was  subjected  to  compressive  stress.  Some  account 
will  be  given  later  of  the  effects  of  stress  on  the  magnetic  quali- 
ties of  iron,  nickel,  and  cobalt ;  meanwhile  it  may  suffice  to 
explain  that  nickel  is  extremely  sensitive  to  stress,  its  suscep- 
tibility being  greatly  reduced  by  tensile  stress,  and  greatly 
increased  by  compressive  stress.  The  upper  and  lower  dotted 
curves  relate  to  compressive  stresses  of  6*8  and  3-5  kilogrammes 
per  square  millimetre  respectively. 


92 


MAGNETISM    IN    IRON. 


§  76.  Permeability  Curves  for  Cobalt. — Fig.  42  shows  in 
the  same  way  two  permeability  curves  for  a  rod  of  cast  cobalt, 
tested  in  a  yoke.  In  this  experiment  the  rod  was  tested  first 
in  ordinary  condition  of  no  stress,  and  then  under  a  series  of 
loads  producing  various  amounts  of  compressive  stress.  The 
full  line  is  the  curve  for  no  load  ;  the  dotted  line  is  for  a  load 
of  16*2  kilogrammes  per  square  millimetre.  The  curves  cross, 
showing  that  under  weak  magnetic  forces  cobalt  has  its  per- 
meability increased  by  the  presence  of  compressive  stress ;  but 


2500 


5000  7500 

Magnetic  Induction  B. 


10000 


Fia.  42.— Permeability  of  Cast  Cobalt. 


under  sufficiently  strong  forces  the  reverse  is  the  case.*  In  a 
later  chapter  it  will  be  shown  that  a  reversal  of  the  effects  of 
stress  also  occurs  in  iron,  f 

*  In  a  Paper  by  Mr.  C.  Chree,  published  in  abstract  in  Proc.  Roy.  Soc., 
December  19th,  1889,  the  same  conclusion  is  stated,  along  with  other  results 
of  experiment  on  the  influence  of  pressure  on  the  magnetic  qualities  of 
cobalt  The  experiments  with  cobalt  described  in  the  text,  and  illustrated 
in  Figs.  39  and  42,  were  made  in  1888  by  the  writer  and  Mr.  W.  Low, 
They  have  not  been  previously  published. 

t  Further  data  relating  to  the  magnetisation  of  cobalt  will  be  found  in 
a  Paper  by  Messrs.  Fleming,  Ashton  and  Tomlinson,  Phil.  Mag.t  Sept., 
1899. 


CHAPTER   V. 


MAGNETIC   HYSTERESIS. 

§  77.  Magnetic  Hysteresis. — The  curves  which  have  been 
drawn  to  show  the  effects  of  cyclic  magnetising  processes  in  iron, 
steel,  nickel,  and  cobalt,  have  this  important  feature  in  common, 
that  there  is  a  tendency  on  the  part  of  the  metal  to  persist  in  any 
magnetic  state  which  it  may  have  acquired.  This  tendency  is 
specially  obvious  whenever  an  alteration  begins  to  be  made  in  the 
characterof  the  magnetising  process.  Thus, when  the  magnetising 
force  has  been  raised  to  its  highest  value,  we  find,  on  beginning 
to  reduce  the  force,  that  the  magnetism  tends  to  remain.  It  does 
not  all  remain,  but  the  rate  at  which  it  disappears  during  with- 
drawal of  the  magnetising  force  is  notably  less  than  the  rate 
at  which  magnetism  was  being  acquired  during  imposition  of 
the  force,  especially  at  the  beginning  of  the  withdrawal.  The 
existence  of  residual  magnetism  when  the  force  is  wholly  with- 
drawn is  one  result  of  this  reluctance  on  the  part  of  the  metal 
to  change  its  magnetic  condition.  But  the  results  of  this 
tendency  go  further.  If,  for  example,  after  withdrawing 
the  magnetising  force,  we  begin  to  re-apply  it,  we  find  in  the 
early  stages  of  the  process  the  same  reluctance  to  change;  the 
metal  begins  to  regain  magnetism,  but  not  so  fast  as  it 
was  losing  magnetism  during  the  last  stages  of  the  removal 
of  the  force.  The  rate,  however,  improves,  and  when  the 
force  has  been  completely  restored  we  find  that  the  piece 
has  recovered  all,  or  nearly  all  (sometimes  even  a  little  more 
than  all),  the  magnetism  it  lost  while  the  force  was  being 
withdrawn.  The  curve  of  magnetisation  comes  again  to  the 
same,  or  nearly  the  same,  point  as  that  from  which  it  started ; 
but  its  path  during  the  process  of  return  differs  entirely  from 
its  path  during  removal  of  the  force.  The  two  curves  form  a 


94  MAGNETISM    IN    IRON. 

loop,  and  any  intermediate  value  of  the  magnetic  force  is  asso- 
liated  with  different  values  of  the  magnetisation  during  the 
two  processes. 

Moreover,  this  description  applies  equally  to  the  effects  of  any 
cyclic  variation  of  magnetic  force,  provided  the  range  through 
which  the  force  is  varied  be  not  exceedingly  small.  Starting 
from  any  condition  of  magnetism  and  of  magnetising  force,  if 
we  remove  and  re-apply  a  part  of  the  force,  or  if  we  apply  and 
remove  a  supplementary  force,  and  repeat  the  process  until  its 
effects  become  cyclic,  we  find  that  the  two  stages  of  the  process 
may  be  represented  by  two  curves,  which  do  not  coincide,  but 
differ  in  a  way  that  may  be  concisely  described  by  saying 
that  there  is  a  tendency,  at  each  change  of  process,  for  the 
preceding  magnetic  condition  to  persist.  The  changes  of  mag- 
netism lag  behind  the  changes  of  force.  To  this  tendency  the 
author  gave  the  name  of  magnetic  hysteresis,  from  VOTC/DCCO,  to 
lag  behind.* 

§  78.  Effects  of  Hysteresis.— Figs.  43  and  44  give  further 
illustrations  of  the  effects  of  magnetic  hysteresis  in  causing 
a  loop  to  be  formed  on  the  curves  of  magnetisation  when  the 
magnetising  force  experiences  any  cyclic  change.  Fig.  43 
refers  to  a  ballistic  test  of  a  ring  of  very  soft  annealed  iron. 
It  shows,  in  addition  to  the  large  loop  produced  by  reversal 
of  the  magnetising  force,  a  smaller  loop  produced  by  its 
removal  and  re-application,  and  also  two  small  loops  formed  by 
pausing  at  points  on  the  steep  part  of  the  demagnetisation 
curve  and  removing  and  re-applying  the  force  there.  In  Fig. 
44  the  effects  are  shown  of  removing  and  re-applying  the  force 
at  a  number  of  successive  points  during  the  magnetisation  of 
a  long  wire  of  soft  annealed  iron.  Many  other  experiments 
have  shown  that  similar  loops  are  formed  when  there  is  partial 
instead  of  complete  withdrawal  of  magnetising  force,  followed  by 
its  re-application,  and  that  steel,  nickel,  and  cobalt  yield  results 
of  the  same  kind.  The  form  of  the  curves  is  found  to  be  not 
materially  different  whether  the  changes  of  magnetising  force 
are  made  to  occur  at  a  moderate  rate  or  excessively  slowly.  In 
other  words,  the  hysteresis  shown  by  these  loops  is  persistent 

*  Proc.  Roy.  Soc.,  No.  216,  1881,  p.  22  ;  Phil.  Trans.,  1885,  p.  524. 


EFFECTS   OF   HYSTERESIS. 


FIG.  45.— Very  Soft  Iron  Ring- 


96 


MAGNETISM   IN   IRON. 


with  regard  to  time.  Even  prolonged  pauses,  during  which  the 
magnetising  force  is  kept  constant  at  values  midway  between 
the  two  extremes  of  the  cycle,  do  not  cause  the  differences  of 
magnetism  due  to  hysteresis  to  disappear,  or  even  to  become 
sensibly  lessened. 

It  is  at  steep  places  of  the  magnetisation  curve  that  the 
effects  of  hysteresis  are  most  apparent.  Starting  from  a  point 
such  as  a  (Fig.  44),  removal  and  re-application  of  the  force 
augments  the  magnetism ;  this  is  because  the  acquisition  of 


13    /«    /5    16    17   18    19  20  21  22  23 


Fia.  44. — Annealed  Iron  Wire.     Length  =400  diameters.    Results  of 
removing  and  reapplying  the  magnetising  force. 

magnetism  in  the  original  ascending  process  was  retarded  by 
hysteresis,  with  the  result  that  any  species  of  disturbance  (such 
as  the  removal  and  re-application  of  the  force)  causes  an  increase. 
If  we  were  to  repeat  the  cyclic  disturbance  by  again  removing 
and  re-applying  the  same  force,  we  should  find  a  small  further 
increase ;  and  it  is  only  after  several  repetitions  of  the  cyclic 
change  of  force  that  its  magnetic  effects  become  strictly  cyclic. 
Every  loop  in  these  diagrams  shows  that  whenever  the  pro- 
cess of  altering  the  magnetic  force  is  reversed  from  a  process 
of  increment  to  a  process  of  decrement,  or  vice  versd,  the 


EFFECTS    OF   HYSTERESIS.  97 

magnetism  begins  to  change  very  slowly  relatively  to  the  change 
of  H,  no  matter  how  fast  it  may  have  been  changing  (in  the 
opposite  direction)  immediately  before.  So  much  is  this  the 
case  that  the  curves,  when  drawn  to  a  scale  so  small  as  the  scale 
of  these  diagrams,  appear  to  start  off  tangent  to  the  horizontal 
line  whenever  the  change  of  H  is  reversed  in  sign.  It  will 
be  shown,  however,  in  the  next  chapter  that  the  initial  gradient 
of  these  curves  is  not  really  zero,  but  a  small  positive  quan- 
tity. At  the  steepest  part  of  the  great  cycle  in  Fig.  43  the 

value  of          is  no  less  than  14,500 ;  in  the  initial  slope  of  one 
d  H 

j  D 

of  the  small  loops  — —   is  probably  less  than  200.     In  other 
d  H 

words,  if  during  the  reversal  of  magnetism  we  pause  at  the 
steepest  part  of  the  curve  and  begin  to  remove  the  magnetic 
force,  the  gradient  of  the  new  curve  may  be  some  70  or  80  times 
less  steep  than  that  of  the  curve  from  which  it  springs. 

An  obvious  effect  of  hysteresis  is  to  prevent  any  simple  rela- 
tion from  existing  between  H  and  B,  or  H  and  I.  To  specify 
the  magnetisation,  we  must  know  not  only  what  value  the 
magnetic  force  actually  has,  but  what  changes  it  has  undergone 
in  reaching  that  value.  Associated  with  any  one  value  of  the 
force  there  is  a  wide  range  of  possible  values  of  B  or  of  I.  By 
a  suitable  choice  of  processes  in  the  application  and  removal  of 
H,  we  may  carry  the  magnetisation  curve  through  any  point 
whatever  within  the  wide  area  enclosed  between  the  curves 
which  correspond  to  reversal  and  re-reversal  of  a  strong  mag- 
netising force.  Hence  the  definition  of  permeability,  as  the 
ratio  of  B  to  H,  or  the  definition  of  susceptibility,  as  the  ratio 
of  I  to  H,  requires  to  be  limited  (as  was  indicated  in  §  21)  by 
the  conditions  (1)  that  the  piece  is  neutral  to  begin  with;  and 
(2)  that  the  magnetising  force,  with  reference  to  which  the  per- 
meability or  susceptibility  is  expressed,  is  to  be  applied  by  simple 
increment  from  zero,  without  passing  at  any  stage  through 
higher  to  lower  values. 

Not  only  may  the  magnetisation  curve  be  made  to  pass 
through  any  specified  point  in  the  area  enclosed  by  the  large 
reversal  curves,  but  it  may  have  more  than  one  gradient  in  pass- 
ing through  the  point.  The  following  is  an  interesting  example 
of  this  effect  of  hysteresis.  Suppose  that  on  the  descending 


98 


MAGNETISM    IN    IRON. 


limb,  P  Q  (Fig.  45),  of  the  main  reversal  cycle  we  have  stopped 
increasing  the  negative  magnetic  force  at  a  point  Q,  so  chosen 
that  when  the  force  is  removed  the  curve  Q  0  passes  through 
the  origin.  When  the  process  Q  0  is  completed,  the  piece  has 
no  magnetism,  and  it  lies  in  a  field  of  no  force.  Tested  in  any 
ordinary  way  it  might  seem  to  be  in  a  perfectly  neutral  state  ; 
but  its  condition  is  far  from  being  the  same  as  that  of  a  virgin 
piece,  or  from  that  of  a  piece  which  has  been  made  neutral  by 
the  process  of  "  demagnetising  by  reversals."  Such  pieces 
show  no  directional  difference ;  their  susceptibility  is  the  same 
whether  the  first  magnetising  force  be  positive  or  negative. 


Fia.  45. 


But  in  this  case  a  positive  force  would  give  the  curve  0  R, 
which  is  a  continuation  of  Q  0 ;  whereas  a  negative  force  would 
give  the  wholly  different  curve  0  S.  The  initial  susceptibility 
in  the  former  case  is  much  greater  than  in  the  latter.  In 
consequence  of  hysteresis  the  piece,  although  destitute  of  actual 
magnetism  and  not  acted  on  by  any  magnetising  force,  retains 
latent  traces  of  the  magnetic  changes  it  has  passed  through, 
which  cause  it  to  show  a  striking  want  of  directional  symmetry 
when  it  is  subsequently  magnetised  in  one  or  the  other  direction. 
Though  there  is  no  external  evidence  that  the  piece  is  anything 
but  neutral,  it  is  much  more  ready  to  take  magnetism  of  an 
opposite  sign  from  that  which  it  last  held  than  to  take  mag- 
netism of  the  same  sign. 


DISSIPATION  OP  ENERGY  THROUGH  MAGNETIC  HYSTERESIS.       99 

§  79.  Dissipation  of  Energy  through  Magnetic  Hysteresis. — 

One  very  important  consequence  of  magnetic  hysteresis  is  that 
changes  of  magnetisation  (on  the  part  of  iron  and  the  other 
magnetic  metals,  all  of  which  exhibit  hysteresis)  involve  a 
dissipation  of  energy.  When  the  magnetism  is  carried  through 
a  cyclic  series  of  values,  by  cyclic  changes  of  the  magnetising 
force,  the  curves  showing  the  relation  of  I  to  H  form  a  loop, 
and  the  area  of  that  loop,  in  other  words,  the  integral  /H  d  I, 
measures  the  amount  of  energy  dissipated  during  the  cycle 
through  hysteresis.* 

Perhaps  the  simplest  way  to  prove  this  is  to  think  of  the 
magnetisation  as  being  produced  by  a  current  in  a  mag- 
netising solenoid,  and  to  consider  the  work  done  by  the  current 
when  the  magnetism  changes.  To  fix  the  ideas,  take  as  the  core 
of  the  solenoid  a  ring  or  very  long  rod,  of  length  I  and  cross- 
section  s,  wound  with  a  solenoid  of  n  turns  per  centimetre,  so 
that  the  whole  number  of  turns  is  I  n.  Say  that  its  magnetic 
induction  is  increased  by  an  indefinitely  small  amount,  d  B, 
in  an  indefinitely  small  time,  dt,  by  increasing  the  mag- 
netising current  to  an  indefinitely  small  extent.  Then  the 
whole  number  of  lines  of  induction  within  the  solenoid  is  in- 
creased by  the  number  s  d  B,  and  the  time-rate  of  this  increase  is 

j  p 
s .     This  induces  in  the  surrounding  solenoid  an  electro- 

dt 

7  rj 

motive  force  equal  to  In  s  —  in  the  direction  opposite  to  that  of 
d  t 

the  current.  The  current  has  accordingly  to  do  work  in  over- 
coming this  opposing  electromotive  force,  over  and  above 
whatever  further  quantity  of  energy  it  expends  in  heating 
the  conducting  wire.  With  this  last  source  of  loss  we  need 
not  concern  ourselves :  we  wish  to  find  the  energy  which  is  spent 
in  producing  magnetisation.  Let  C  be  the  mean  value  which 

*  This  was  first  shown  by  Warburg  in  an  important  paper  dealing  with 
several  effects  of  magnetic  hysteresis,  Wied.  Ann.,  XIII.  (1881),  p.  141. 
He  proved  it  by  supposing  the  magnetic  force  to  depend  upon  the  position 
of  permanent  magnets,  and  by  calculating  the  work  spent  in  carrying  these 
magnets  through  the  necessary  cyclic  changes  of  position.  It  was  after- 
wards discovered  independently  by  the  writer  (Proc.  Roy.  Soc.,  May,  1882, 
No.  220,  p.  39  ;  Phil.  Trans.  1885,  p.  549).  The  method  of  proof  followed 
in  the  text  is  substantially  Hopkinson's,  Phil.  Trans.,  1885,  p.  466 :  we 
also  Lord  Rayleigh,  Phil.  May.,  Vol.  XXII.,  p.  176. 

H2 


100  MAGNETISM   IN   IRON. 

the  current  has  during  the  time  dt.  The  opposing  electro- 
motive force,  due  to  the  change  of  magnetic  induction  in  the 
core,  when  multiplied  by  the  current  and  by  the  time  dt, 
gives  the  quantity  of  work  done  by  the  current.  Hence  the 
work  done  by  the  current  in  producing  the  change  of  mag- 
netism d  B  is 

lk*  —  Gdttorln$GdB. 

dt 

The  fact  that  d  t  disappears  shows  that  this  work  does  not 
depend  on  the  time-rate  at  which  the  change  of  induction  takes 
place ;  we  have  the  same  quantity  of  energy  used  in  the  pro- 
cess whether  the  change  d  B  takes  place  fast  or  slowly.  Since 
the  volume  of  the  core  is  I  s,  we  may  write  d  W,  the  work  done 


by  the  magnetising  current  per  unit  of  volume  (that  is,  per 
cubic  centimetre),  hi  bringing  about  the  change  d  B,  as 

nCdB. 
But  the  magnetising  force  H  is  4  TT  C  n,  hence 


To  obtain  the  work  done  per  cubic  centimetre  of  the  metal 
when  B  is  changed  by  any  finite  amount  by  changing  the  mag- 
netising force  from  (say)  a  value  h^  to  another  value  H2  we  have 
to  integrate  this  expression,  finding 


between  the  limits  H2  and  Hr 

Thus,  in  Fig.  46,  if  P  and  Q  are  any  two  points  in  the  curve 
of  B  and  H,  the  work  done  per  cubic  centimetre  as  the  mag- 
netic state  alters  from  P  to  Q  is  the  area  M  P  Q  N  divided  by 


DISSIPATION  OF  ENERGY  THROUGH  MAGNETIC  HYSTERESIS.    101 


4  TT.  For  example,  in  magnetising  a  piece  which  has  no  mag- 
netism to  begin  with,  the  curve  followed  being  0  P  (Fig.  47), 
the  work  done  in  reaching  P  is  equal  to  the  area  0PM 
divided  by  4  TT.  If  we  then  remove  the  magnetising  force  (curve 
P  R)  we  recover  a  quantity  of  work  equal  to  the  area  R  P  M, 
divided  by  4  TT;  the  net  expenditure  of  energy  in  the  whole  pro- 
is,  therefore,  equal  to  the  shaded  area  OPE,  divided  by  4  TT. 


°  H 

FIG.  47. 

In  this  case  the  final  state  of  the  metal  at  R,  is  different  from 
its  initial  state  at  0,  and  it  is  therefore  not  immediately  obvious 
how  much  of  this  energy  has  been  spent  irrecoverably.  But 
let  a  cyclic  process  be  followed,  so  that  at  the  end  the  magnetisa- 
tion, as  well  as  the  magnetising  force,  is  brought  back  to  the 
value  it  had  at  the  beginning ;  in  that  case  there  can  be  no 
accumulation  of  recoverable  energy  at  the  end  of  the  cycle. 


B 


H 

FIG.  48. 

The  whole  difference  between  what  is  spent  during  one  part  of 
the  process  and  what  is  recovered  during  the  other  part  is 
therefore  dissipated,  and  simply  goes  to  heat  the  metal.  Thus, 
when  we  carry  the  metal  through  any  cyclic  series  of  magnetic 
changes — such,  for  instance,  as  are  represented  in  Fig.  48, 
where  the  magnetising  force  is  removed  and  reapplied,  or  in 


102 


MAGNETISM  IN  IRON. 


Fig.  49,  where  it  is  reversed  and  re-reversed  —  there  is  a  quan- 
tity of  energy  dissipated  in  each  cycle  which  is  equal,  per  cubio 

centimetre  of  the  metal,  to  —  /  H  d  B  :  in  other  words,  it  is 

4-n-J 

equal  to  the  shaded  area  enclosed  by  the  curves   connecting 
H  and  B,  divided  by  4  TT. 
Moreover,  since  c£B  =  47rc 


~-{HdB  =  (  Hd\+  -If 

4:TTj  J  4.TTJ 


But  in  a  cyclic  process,  /HdH   vanishes;  and  the   energy 
dissipated  in  a  cycle  is,  therefore, 

fHd\ 


FIG.  49. 

Thus  in  Figs.  48  and  49,  if  we  represent  the  magnetism  by  I 
instead  of  by  B,  the  shaded  area  measures  the  amount  of 
energy  dissipated  in  each  cubic  centimetre  of  the  magnetised 
metal  during  the  cyclic  process  which  the  curves  represent. 

As  C.-G.-S.  units  are  used  in  expressing  H  and  I,  the  area 
within  the  curves  gives  the  energy  dissipated  (per  cubic  centi- 
metre) in  C.-G.-S.  units  of  work,  or  ergs. 

§  80.  Heating  Effect  of  a  Cyclic  Process. — The  dissipated 
energy  takes  the  form  of  heat :  hence  iron  and  other  metals  in 


HEATING   EFFECT   OF   A   CYCLIC   PROCESS.  103 

which  there  is  magnetic  hysteresis  become  warmed  when  their 
magnetism  is  successively  reversed  or  varied  in  any  way  —  the 
effect  of  reversal  being  much  more  marked  than  the  effect  of 
simple  removal  and  reapplication  of  a  magnetising  force,  because 
of  the  much  greater  area  of  the  reversal  loops. 

The  iron  of  transformers  and  the  cores  of  dynamo-armatures 
are  familiar  instances  in  point.  The  heating  which  occurs  as 
a  consequence  of  hysteresis  has,  of  course,  nothing  to  do  with 
the  additional  heating  which  Foucault  or  eddy  currents  may 
cause  when  quick  changes  of  magnetism  are  made  to  take  place 
in  iron  which  is  not  sufficiently  laminated.  Hysteresis  causes 
heating  however  slowly  the  magnetism  changes,  and  however 
minute  are  the  subdivisions  of  the  core. 

To  find  the  rise  of  temperature  which  a  magnetic  metal  suffers 
when  its  magnetism  is  cyclically  varied,  we  have  to  reduce  the 
value  of/  H  d  I  to  thermal  units,  and  divide  by  the  number  of 
grammes  in  a  cubic  centimetre,  and  by  the  specific  heat.  Using 
centigrade  degrees,  there  are  41,600,000  ergs  in  a  thermal  unit. 
In  iron,  the  specific  heat  is  0-11,  and  there  are  7*7  grammes  in 
a  cubic  centimetre.  Hence,  the  rise  of  temperature  caused  by 
a  magnetic  cycle  is  — 


§  81.  Values  of  /H  d  I.—  In  soft  annealed  iron  the  value  of 
/  H  d  I,  for  each  double  reversal  of  a  condition  of  strong 
magnetization,  is  about  10,000  ergs.  Nearly  4,000  double 
reversals  would  therefore  be  necessary  to  raise  the  temperature 
of  a  soft  iron  core  by  1°  C.,  if  the  influence  of  eddy  currents 
could  be  excluded. 

Since  there  are  7  '7  grammes  of  iron  in  1  cubic  centimetre, 
and  453*6  x  2240  grammes  in  a  ton,  the  energy  dissipated  in 
taking  one  ton  of  iron  through  a  magnetic  cycle  is 

453-6  x  2240  x/hU  I 

7-7 

Suppose  that  there  are  »  cycles  per  second  :  the  work  done  in 
ergs  per  second  is  then 

nx  453-6  x  2240  x/Hd\ 

7-7 


104  MAGNETISM   IN    IRON. 

We  may  reduce  this  to  horse-power  by  dividing  by  7*46  x  109, 
which  is  the  number  of  ergs  per  second  in  1  horse-power.  Hence 
the  horse-power  consumed  through  magnetic  hysteresis  when 
one  ton  of  iron  is  taken  repeatedly  through  a  set  of  cyclic 
changes  of  magnetism  at  the  rate  of  n  cycles  per  second  is 

0-00001769  nfHd  I. 

Applying  this  to  the  case  of  soft  annealed  iron,  where 
/  H  d  I  for  double  reversals  of  strong  magnetisation  is  about 
10,000  C.-G.-S.  units,  the  horse-power  per  ton,  for  100  cycles 
of  double  reversal  per  second,  is  17*7. 

In  harder  specimens  of  annealed  wrought-iron  the  value  of 
/  H  d  I  for  a  double  reversal  of  strong  magnetism  may  be  as 
much  as  16,000.  Hardening  the  metal  by  mechanical  strain 
increases  the  area  within  the  curves,  as  a  reference  to  Figs.  34 
and  38  will  show.  In  mild  steel  Hopkinson's  experiments* 
show  that  the  value  ranges  from  that  found  in  wrought  iron  up 
to  40,000  or  even  60,000 ;  it  increases  in  a  general  way  with 
increase  in  the  percentage  of  carbon,  and  is  greater  in  speci- 
mens which  are  hardened  by  quenching  than  in  thpse  which 
have  a  lower  temper.  In  high  carbon  steels  the  valut'  may  ex- 
ceed 60,000.  In  pianoforte  steel  wire  94,000  has  been  obtained 
when  the  metal  was  annealed,  116,000  when  in  its  commercial 
state,  and  117,000  when  hardened  by  quenching  in  water  from 
a  red  heat.  Chrome  steel  (containing  about  1  per  cent,  of 
chromium)  ranged  from  about  65,000  (annealed)  to  167,000 
(oil-hardened).  In  tungsten  steel  Hopkinson  found  even  higher 
values ;  an  oil-hardened  French  specimen  containing  3 '4  per 
cent,  of  tungsten,  0'5  per  cent,  of  carbon,  and  0-6  per  cent,  of 
manganese,  consumed  216,800  ergs,  or  more  than  twenty  times 
the  amount  consumed  in  soft  wrought-iron.  The  dissipation 
of  energy  in  a  cycle  of  double  reversal  is  roughly  equal  to  four 
times  the  coercive  force  multiplied  by  I. 

In  cast-iron,  values  of  30,000  to  40,000  appear  to  be  usual ; 
but  in  one  sample  of  soft  grey  cast-iron  Hopkinson  has  found 
so  low  a  value  as  13,000.  In  nickel,  a  hard-drawn  wire  gave 
25,000,  which  was  reduced  to  11,000  when  the  wire  was 
annealed.  Thus  the  dissipation  of  energy  in  nickel  when  a 
strong  magnetising  force  is  reversed  is  much  the  same  as  that 

*  Phil.  Trcms.,  1885,  p.  463. 


DISSIPATION   OF   ENERGY   BY   REVEESALS.  105 

in  wrought-iron,  the  greater  coercive  force  of  nickel  being 
counterbalanced  by  the  lower  intensity  of  magnetism  it  is 
capable  of  reaching,  even  when  "  saturated."  As  regards  cobalt, 
the  experiment  with  a  cobalt  rod  containing  two  per  cent,  of 
iron,  described  in  §  72  and  shown  in  Fig.  39,  gives  30,400  as 
the  value  of/H  dl 

§  82.  Dissipation  of  Energy  by  Eeversals  of  Moderately 
Strong  Magnetisation. — When  the  intensity  of  magnetism 
at  which  reversal  takes  place  is  reduced,  the  energy  dissipated 
is,  of  course,  less  than  has  been  stated  in  §  81,  where  the 
numbers  given  for  /  H  d  I  refer  to  reversals  of  a  magnetic 
state  approaching  saturation.  Fig.  50  shows  the  effect  of 
subjecting  a  piece  of  soft  annealed  iron  wire  to  a  graded  series 
of  reversals  beginning  with  weak  forces,  and  gradually  in- 
creasing the  force  till  the  limits  of  H  were  ±75  C.-G.-S.* 
Parts  of  the  curves  relating  to  strong  forces  are  omitted 
in  the  figure.  The  wire  was  0 -078cm.  in  diameter  and  29cm. 
long,  and  was  tested  by  the  direct  magnetometric  method ; 
between  300  and  400  observations  of  the  relation  of  H  to  I 
were  required  to  define  the  curves  in  the  ten  successive 
processes  of  double  reversal  which  are  represented  in  the 
figure.  In  Table  V.  the  numbers  in  the  first,  second  and  third 
columns  are  the  values  of  H,  of  B,  and  of  I,  between  which  the 
successive  double  reversals  took  place  ;  the  next  column  gives 
the  energy  dissipated  per  cycle  in  ergs  per  cubic  centimetre, 
found  by  measuring  the  areas  enclosed  within  the  curves,  and 
the  last  shows  the  rise  of  temperature  which  a  complete  cycle 
should  produce. 

These  results  are  shown  in  Fig.  51  by  plotting  the  measured 
values  of/  H  d\  in  terms  of  the  induction,  B,  at  which  each 
double  reversal  took  place.  It  will  be  seen  from  this  curve  that 
the  waste  of  energy  increases  rapidly  as  B  is  raised,  which  is  a 
reason  for  avoiding  high  induction  in  the  cores  of  transformers, 
and  in  the  armatures  of  alternate-current  dynamos.  With  low 
intensities  of  magnetism  the  waste  is  less  than  proportionally 
small.  Table  VI.  gives  numerical  values  taken  from  the  curve 
of  Fig.  51,  along  with  the  horse-power  wasted  per  ton  of  iron, 

*  From  a  Paper  by  the  Author,  Phil.  Trans.,  1885,  p.  555. 


106 


FIG.  50.— Graded  Cyclic  Mag 
netisations  of  Soft  Iron. 


1200 


DISSIPATION   OF   ENERGY   BY    REVERSALS. 


107 


if  100  cycles  (that  is,  200  separate  reversals)  are  completed  per 
second.* 


10,000 
9,000 
8,000 
7,000 
6,OOD 
5,0:0 
4,000 
3,000 
2,000 
1,000 

« 

/ 

r 

•f 

f 

/ 

* 

/ 

A 

X 

x 

xr 

x 

^ 

s* 

^-* 

^ 

3000000000000000« 

S     3     S     3 


of  B- 


FIG.  51.— Dissipation  of  Energy  in  Soft  Iron  through  Magnetic  Hysteresis 
in  Double  Reversals  of  Magnetisation. 


TABLE  V. — Graded  Cyclic  Magnetisations  of  Soft  Iron. 
(Fig.  50.) 


H 

B 

\ 

rud\ 

Calculated  rise  of 
temperature. 

ergs. 

deg.  C. 

1-50 

1,974 

167 

410 

0-000012 

1-95 

3,830 

304 

1,160 

0-000033 

2-56 

5,950 

473 

2,190 

0-000062 

3-01 

7,180 

571 

2,940 

0-000083 

3-76 

8,790 

699 

3,990 

0-000113 

4-96 

10,590 

842 

5,560 

0-000158 

6-62 

11,480 

913 

6,160 

0-000175 

7-04 

11,960 

951 

6,590 

0-000187 

26-5 

13,720 

1090 

8,690 

0-000247 

75-2 

15,560 

1230 

10,040 

0-000285 

*  See  also  Mr.  Kapp's  Paper  on  "  Alternate-Current  Machinery  "  (Min. 
Proc.  Inst.  C.E.,  Feb.,  1889),  where  a  similar  table  is  given,  calculated  from 
the  same  experiment. 


108 


MAGNETISM    IN   IRON. 


TABLE 


-Dissipation    of  Energy  by  Double   Bevertals   of 
Magnetism  in  Soft  Iron. 


B 

/HcH  (ergs). 

Horse-power  wasted  per 
ton  assuming  100  cycles 
per  second. 

2,000 

420 

074 

3,000 

800 

1-41 

4,000 

1,230 

2-18 

5,000 

1,700 

3-01 

6,000 

2,200 

3-89 

7,000 

2,760 

4-88 

8,000 

3,450 

6-10 

9,000 

4,200 

7-43 

10,000 

5,000 

8-84 

11,000 

5,820 

10-30 

12,000 

6,720 

11-89 

13,000 

7,650 

13-53 

14,000 

8,650 

15-30 

15,000 

9,670 

17-10 

Fig.  52*  shows  the  results  of  a  corresponding  experiment 
made  with  a  specimen  of  annealed  pianoforte  steel  wire.  Here 
much  the  same  features  present  themselves.  When  the  mag- 
netisation is  feeble  there  is  but  little  dissipation  of  energy, 
but  as  the  range  of  I  is  extended  the  area  of  the  loops  increases 
fast. 

Fig.  53 f  exhibits,  in  a  different  way,  the  results  of  these  two 
experiments  on  iron  and  steel.  The  heating  effect  of  a  cycle 
(calculated  from  /H  d  I)  is  shown  in  relation  to  the  value  of  H 
which  was  reversed.  At  first  the  heating  effect  of  reversal  is 
much  less  in  steel  than  in  iron,  with  a  given  value  of  H,  for 
the  smaller  susceptibility  of  steel  makes  the  whole  magnetic 
change  comparatively  small.  But  with  stronger  fields  its 
greater  coercive  force  begins  to  tell,  and  the  heating  effect 
becomes  at  last  very  much  greater  in  steel  than  in  iron. 

§83.  Influence  of  Speed  on  Magnetic  Hysteresis. — It 
appears  in  general  that  the  speed  at  which  a  cycle  of  mag- 

*  Phil.  Trans.,  1885,  p.  556. 

f  Copied  from  a  Paper  by  A.  Tanakadatd  "  Oa  the  Thermal  Effect  due  to 
Reversals  of  Magnetisation  in  Soft  Iron,"  Phil.  Mag.,  Sept.,  1899. 


INFLUENCE   OF  SPEED   ON   MAGNETIC   HYSTERESIS. 


109 


netisation  is  performed  has  no  very  material  effect  on  the 
value  of /He?  I,  provided  that  the  iron  be  sufficiently  laminated 
to  escape  the  effects  of  Foucault  currents.  In  certain  cases 
speed  is  known  to  have  an  effect.  In  the  next  Chapter  results 


FIG.  52. — Graded  Cyclic  Magnetisations  of  Annealed  Pianoforte  Steel  Wire 

will  be  described  which  show  that  when  bars  of  soft  iron  are 
subjected  to  very  small  cyclic  changes  of  H  the  corresponding 
magnetic  changes  depend  very  largely  upon  the  speed  at  which 
H  is  varied.  There  does  not  appear  to  be  anything  like  so 
serious  a  dependance  on  speed  when  the  magnetic  changes  are 


110 


MAGNETISM   IN   IRON. 


OOOiS 


•ooe 


considerable ;  and  it  appears  probable  that  results  obtained 
from  experiments  on  the  observed  relation  of  I  to  H  when  H  ia 
changed  very  slowly  are  substantially  applicable  when  H  is 
changed  fast.  With  regard  to  small  changes  of  magnetising  force, 

however,  soft  iron  exhibits 
what  may  be  called  magnetic 
viscosity — that  is  to  say,  the 
changes  of  magnetism  follow 
somewhat  sluggishly  thechanges 
of  magnetising  force,  just  as  in 
the  stretching  and  unstretching 
of  a  rod  of  india  rubber  by  apply- 
ing and  removing  weights,  the 
changes  of  length  follow  slug- 
gishly the  changes  of  load.  If 
this  property  exists  to  any  con- 
siderable degree  in  cases  where 
the  range  of  magnetic  change  is 
wide,  it  may  have  the  effect  of 
causing  fHd I,  in  a  quickly  per- 
formed cycle,  to  differ  from  the 
value  observed  in  such  experi- 
ments as  have  been  described. 

The  whole  question  of  mag- 
netic viscosity  is  one  of  great 
practical  interest.  Attempts  to 
investigate  it  by  making  direct 
calorimetric  measurements  of 
the  heat  generated  by  magnetic 
reversals  present  a  good  deal 
of  difficulty.  They  have  been 
made  by  more  than  one  observer, 
but  the  experiments  hitherto 
carried  out  cannot  be  said  to 
settle  the  question  raised  above,  Warburg  and  Honig,*  experi- 
menting with  bundles  of  fine  wires  (to  get  rid  of  Foucault 
currents),  found  that  the  heating  effect  of  reversals,  as 
measured  in  a  calorimeter,  was  about  two-thirds  of  the  value 

*  Wied.  Ann.,  1883,  Vol.  XX.,  p.  814. 


Values  or  H. 

FIG.  53. 

Heating  Effect  of  Reversals  of  Mag- 
netising Force  in  Iron  and  Steel. 


STEINMETZ    CO-EFFICIENT   OP   HYSTERESIS.  Ill 

of  /He?  I,  as  calculated  from  magnetic  observations  in  slow 
cycles.  Tanakadate*,*  using  a  multiple  ring  of  cotton-covered 
soft-iron  wire,  and  measuring  the  heat  developed  in  it  by 
reversals,  by  noting  the  rise  in  temperature  of  a  thermo-electric 
junction  placed  under  the  magnetising  coil,  found  the  heating 
effect  of  quick  cycles  to  be  equivalent  to  about  80  per  cent,  of 
the  slow-cycle  value  of  /H  d  \.  He  observed,  further,  that  the 
heating  effect  was  practically  independent  of  the  frequency  of 
the  reversals  when  that  was  varied  between  the  limits  of  28 
and  400  cycles  per  second.  A  chief  difficulty  in  observations 
of  this  class  is  to  determine  what  is  the  actual  value  which  H 
reaches  during  rapid  alternations  of  the  magnetising  current. 
Though  these  results  are  subject  to  some  uncertainty,  they 
concur  in  making  it  probable  that,  for  a  given  value  of  alter- 
nating H,  the  range  of  magnetisation  is  less  in  quick  alter- 
nations than  in  static  experiments  (where  the  reversal  goes 
on  slowly  or  by  steps  with  pauses  between),  and  hence  that 
the  dissipation  of  energy  is  less  in  a  quick  cycle  on  account  of 
this  diminished  range  of  magnetic  change. 

§  83a.  Steinmetz  Co-efficient  of  Hysteresis.  —  By  examining 
in  a  number  of  specimens  of  iron  the  relation  between  the  work 
spent  on  hysteresis  and  the  extreme  magnetic  induction 
reached  in  the  cycle  Mr.  Steinmetz  t  has  obtained  an 
empirical  formula  which,  although  it  fails  to  apply  when  the 
magnetisation  is  very  weak  or  very  strong,  may  be  used  as  a 
good  approximation  throughout  the  range  of  magnetisation 
generally  employed  in  electrical  engineering.  Within  that 
range  his  results  show  that 


where  t\  is  a  factor,  constant  for  any  one  specimen,  called  the 
coefficient  of  hysteresis,  and  n  is  a  general  constant,  the  value 
of  which  Mr.  Steinmetz  gives  as  1-6.  The  author  finds  that 
1'59  corresponds  more  exactly  with  the  data  he  has  accumu- 
lated for  sheet  iron.  It  appears  that  this  index  has  a  value 
which  approximates  to  1-6  not  only  in  specimens  of  highly 

*  Phil.  Mag.  ,  Sept.,  1889. 

t  Steinmetz,  Trams.  American  Institute  of  Electrical  Engineers,  Jan.  19, 
1892. 


11$  MAGNETISM   IN    IRON. 

permeable  material,  such  as  wrought  iron,  but  also  In  other 
magnetic  metals.  Experiments  by  Miss  Klaassen  and  the 
author*  have  shown  that  it  holds  with  fair  accuracy  for  widely 
different  specimens  of  iron  and  steel.  Dr.  Kennelly  has  shown 
that  it  applies  approximately  in  the  case  of  nickel. t  Professor 
Fleming  and  Messrs.  Ashton  and  Tomlinson  have  done  the 
same  for  cobalt.  J  Except  in  cast  iron,  where  the  value  of  n 
appears  to  be  considerably  greater,  we  may  take  the  formula 

Hysteresis  loss  in  a  cycle  =  rj  B 1 6 

as  fairly  correct  for  those  values  of  B  ordinarily  reached  in 
dynamos  and  transformers.  The  coefficient  rj  may  be  as  low 
as  0*001  in  good  transformer  iron.  The  following  table  gives 
its  value  in  a  number  of  examples  : — 

Hysteresis  Coefficient  t\ 

Soft  iron  wire  of  Fig.  50    ..».     0'0020 

Sheet  iron  for  transformers  ... O'OOIO  to  0-0012 

Common  sheet  iron     ,.. 0"003 

Sheet  steel  for  transformers O'OOll 

High  carbon  steel,  hardened 0"025 

„  „        annealed  O'OOS 

Cobalt,  Cast     O'Ol 

Further  data  for  the  sheet  iron  used  in  transformers  and 
dynamo  armatures  will  be  found  in  Papers  by  the  author 
and  by  Mr.  H.  F.  Parshall  on  the  "Magnetic  Testing  of  Iron 
and  Steel,"  published  by  the  Institution  of  Civil  Engineers.§ 

Examples  of  graded  hysteresis  cycles  in  various  specimens  of 
iron  and  steel  are  given  in  the  Paper  by  Miss  Klaassen  and  the 
author  to  which  reference  has  been  made  above. 

The  hysteresis  losses  in  iron  are  occasionally  stated  as  so 
many  watts  per  Ib.  for  a  frequency  of  100  cycles  per  second. 
Taking  the  specific  gravity  of  the  iron  to  be  7 '7  the  factor  for 
reducing  ergs  per  cubic  centimetre  into  watts  per  Ib.  at  a 
frequency  of  100  is  0-000589. 

§  84.  Effects  of  Vibration. — The  influence  of  vibration  and 
mechanical  disturbance  generally  upon  magnetic  quality  has 

*  Phil.  Trans.,  1894. 

t  Electrician,  Vol.  XXVIII.,  p.  666.     t  Phil.  Mag.,  Sept.,  1899. 

$  Min.  Proc.  Inst.  C.E.,  Vol.  CXXVL,  May,  1896. 


EFFECTS    OF    VIBRATION. 


113 


been  shortly  referred  to  in  §  64  ;  it  may  be  succinctly  described 
by  saying  that  vibration  lessens  those  differences  of  magnetic 
condition  to  which  hysteresis  gives  rise.  Thus,  if  we  tap  a  piece 
of  iron  during  the  application  and  removal  of  magnetising 
force,  we  find  at  each  stage  of  the  application  that  tapping 
increases  the  susceptibility,  and  at  each  stage  of  the  removal  it 
reduces  the  retentiveness.  Whatever  be  the  exact  nature  of 
the  molecular  rearrangement  which  constitutes  magnetisation 
it  is  facilitated  by  vibration,  which  may  be  imagined  to  act  by 
setting  the  molecules  momentarily  free,  more  or  less,  from  the 
constraint  in  which  they  ordinarily  lie.  An  analogy  may  be 
drawn  to  the  way  in  which  iron  turnings  scattered  on  a  table 
near  a  magnet  are  freed  to  range  themselves  along  the  lines 
of  magnetic  force  when  the  table  is  tapped ;  but  it  must  not 
be  inferred  that  the  constraint  of  the  magnetic  molecules  has 
anything  of  the  quality  of  mechanical  friction.  What  that 
constraint  probably  is  will  be  discussed  in  a  later  chapter. 

In  strong  fields  the  influence  of  vibration  is  scarcely  felt ;  in 
weak  fields  it  is  often  enormous.  The  effect  in  a  weak  field  is 
well  shown  by  the  familiar  experiment — described  by  Gilbert 
nearly  three  hundred  years  ago — of  magnetising  a  bar  of  iron  by 
hammering  it  while  it  is  exposed  to  the  earth's  magnetic  force. 
Let  the  bar,  for  instance,  be  held  upright :  the  vertical  com- 
ponent of  the  terrestrial  field  is  too  weak  to  produce  more  than 
the  feeblest  trace  of  magnetism  so  long  as  there  is  no  mechanical 
disturbance.  WThen  sharply  tapped,  however,  it  becomes  a  fairly 
strong  magnet,  and  the  magnetism  taken  up  in  this  way  will 
persist  after  the  bar  has  been  withdrawn  from  the  field,  until 
it  is  expelled  by  further  tapping  or  by  the  application  of  a 
moderately  strong  magnetic  force  of  the  opposite  sign.  The 
magnetism  acquired  by  an  iron  ship  in  building  is  another  in- 
stance in  point,  and  still  another  is  the  magnetism  which  the 
shock  of  rupture  produces  in  a  specimen  of  iron  or  steel  broken 
in  a  testing  machine.  Vibration  affects  all  the  magnetic  metals 
more  or  less,  but  it  is  in  soft  annealed  iron  wire  that  its 
influence  is  most  remarkable.  Gentle  rubbing  will  give  much 
magnetism  to  a  soft  iron  wire  suspended  in  the  terrestrial  field, 
or  will  take  away  much  of  the  large  residue  which  persists  after 
a  strong  magnetising  force  has  ceased  to  act.  Much  care  is,  in 
fact,  necessary  in  experiments  on  the  susceptibility  or  retentive 


114 


MAGNETISM    IN    IRON. 


ness  of  this  material  to  avoid  serious  errors  through  accidental 
disturbance  of  the  specimen.  The  effects  of  hysteresis  almost 
entirely  vanish  in  the  magnetisation  of  soft  iron  wire,  if  the 
piece  be  briskly  tapped  during  application  and  removal  of  the 
magnetising  force.  The  curves  of  I  and  H  or  B  and  H  in 
the  two  processes  become  nearly  coincident,  and  the  relation 
of  magnetism  to  magnetising  force  becomes  comparatively 
determinate.  Two  experiments  may  be  quoted  to  show  these 
effects.* 

§  85.  Experiments  on  the  Effects  of  Vibration  in  the 
Magnetisation  of  Soft  Iron  Wire. — The  wire  was  a  piece  of 
very  soft  annealed  iron,  0*158cm.  in  diameter,  and  64cms.,  or 
400  diameters  long,  of  the  same  quality  as  that  tested  in  the 
experiments  of  §  64.  The  test  was  made  by  the  ballistic 
method ;  the  magnetising  force  was  raised  by  steps,  and  after 
each  step  the  wire  was  vigorously  beaten  against  the  table, 
and  the  magnetism  was  then  measured  by  slipping  off  a 
movable  induction  coil.  Observations  were  made  in  the  same 
way  at  a  series  of  stages  during  the  removal  of  the  force. 
Table  VII.  gives  the  values  of  B  found  after  tapping,  first, 
during  application,  and  then  during  removal  of  the  force,  when 
the  magnetising  force  due  to  the  solenoid  had  the  values  stated 
in  the  first  column. 

TABLE  VII. — Magnetisation  of  Soft  Iron  Wire  with  Vibration. 


Magnetising  Force 
due  to  Solenoid. 

B 

During  Application. 

B 

During  Eemoval. 

0 

240  (initial) 

400 

0-04 

840 

1,440 

0-15 

3,370 

— 

0-31 

5,370  m 

5,850  f 

0-62 

8,260  I 

8,500  ft 

0-96 

9,540 

9,860 

1-60 

10,740 

11,200 

2-92 

12,040 

12,400 

5-04 

13,140 

13,000 

7-00 

13,460 

13,550 

16'8 

14,750  »-> 

From  a  Paper  by  the  Author,  Phil.  Trans.  Roy.  Soc.,  1885  p.  564 


EXPERIMENTS    ON    THE    EFFECTS    OF    VIBRATION. 


115 


A  glance  at  these  figures  will  show  the  enormous  increase  of 
susceptibility  brought  about  by  tapping.  A  force  of  0'96  in 
the  solenoid,  with  tapping,  brings  B  up  to  9,540;  but  another 
experiment  on  the  same  piece  of  wire  showed  that  without 
tapping  the  value  of  B  under  the  same  force  was  only  550.  In 
Fig.  54  curves  are  drawn,  with  a  very  open  scale  of  H,  to  illus- 
trate the  portions  of  this  experiment  which  deal  with  feeble  mag- 
netic forces.  The  full  line  0  P  refers  to  the  application  of  mag- 
netic force,  and  the  dotted  line  above  it  to  the  removal  of  the 


,000 

9,000 
8,000 
7,000 
6,000 
5,000 
4,000 
3.000 
2,000 
1,000 


0      01      0-2     0-3    0-4     0-5     0'6     07     0'8     0'9     I'O     I'l     T2    1'3 
Magnetising  Force  due  to  Solenoid  (C.Q.S.). 

Fio.  54. — Magnetisation  of  Soft  Iron  Wire  ;  0  P,  with  vibration, 
O  Q,  without  vibration. 

force,  both  with  tapping ;  while  the  line  0  Q  refers  to  the  appli- 
cation of  magnetic  force  without  tapping.  The  magnetic  force 
plotted  here  is  that  due  to  the  solenoid  alone,  but  it  is  impor- 
tant to  notice  that  this  is  by  no  means  the  true  total  force  in 
the  experiment  made  with  vibration.  Though  the  wire  is  400 
diameters  long,  it  cannot  be  treated  as  sensibly  endless.  The 
reaction  of  the  ends  becomes  very  important  on  account  of  the 
excessively  great  susceptibility.  The  real  field  is  much  less 
than  the  field  due  to  the  solenoid — how  much  less  may  be 
judged  from  the  line  0  A,  which  is  drawn  (in  the  manner 

J2 


116 


MAGNETISM  IN  IRON. 


described  in  §  48)  on  the  supposition  that  the  wire  may  fairly 
be  treated  as  an  ellipsoid  400  times  as  long  as  it  is  broad.  On 
this  supposition  the  true  magnetic  force  is  to  be  found  by 
measuring  the  horizontal  distance  of  any  point  in  the  curves 
from  the  line  0  A.  Even  neglecting  this  correction  of  the 
magnetic  force  the  ratio  of  B  to  the  (solenoid's)  force  is  not  less 
than  20,000  in  the  initial  part  of  the  curve  ;  and  after  allowing 
for  the  influence  of  the  ends  of  the  specimen  by  measuring  the 
magnetic  force  from  the  line  0  A  the  permeability  is  found  to 
have  the  enormous  value  of  about  80,000.  The  permeability  is 
greatest  at  or  near  the  beginning  of  the  magnetising  process ;  the 


14,000 
12,000 
10,000 
8,000 
6,000 
4,OOC 
2,000 



as 

— 

— 

... 

,*' 

'"'*' 

..^ 

^ 

•'/ 

f,.- 

^ 

I/a 
II 

/ 

/ 

| 

i 

II 
i 

1 

S 

' 

0        1       2       3       4       5       6       7       8       9      10      11      12     13     14     15     16     17 
Magnetising  Force  due  to  Solenoid. 

FIG.  55. — Magnetisation  of  Very  Soft  Annealed  Iron  Wire.    Without 

tapping,  ;  with  tapping, ;   continuation,  without 

tapping,  after  reaching  (with  tapping)  the  point  a, 


concavity,  which  is  a  feature  in  the  early  part  of  curves  deter- 
mined without  tapping,  has  nearly,  if  not  quite,  disappeared. 

The  complete  experiment  is  shown  in  Fig.  55.  The  curves  shown 
by  full  lines  were  obtained  by  applying  and  removing  a  mag- 
netising force  of  nearly  17  units  without  vibration.  The  curves 

shown  thus refer  to  the  same  process  performed  with 

vibration.  Finally,  after  magnetising  again  to  the  point  a  with 
vibration,  the  application  of  magnetic  force  was  continued 
without  vibration,  and  the  results  of  this  are  shown  by  the  dotted 

curve  It  is  interesting  to   notice  how  the  effects  of 

hysteresis  immediately  re-assert  themselves  when,  after  tapping, 
we  continue  the  magnetising  process  with  the  specimen  at  rest. 


EXPERIMENTS    ON    THE    EFFECTS    OF   VIBRATION. 


117 


In  another  experiment,  with  the  same  piece  of  wire,  the 
magnetic  force  was  raised  to  a  certain  value,  without  vibra- 
tion, while  B  was  determined  ballistically;  then  the  wire  was 
smartly  tapped,  and  the  change  which  B  underwent  through 
the  tapping  was  measured  by  slipping  off  the  induction  coil; 
then  the  coil  was  replaced,  and  the  force  was  raised  by 
steps  to  a  higher  value;  then  the  wire  was  again  tapped, 
and  so  on.  The  wire  had  an  initial  magnetism  (B)  of  170, 
which  rose  to  190  when  a  force  of  0'32  was  applied  with- 
out tapping;  then,  while  this  force  continued  to  act,  tapping 
brought  up  the  value  of  B  at  a  bound  to  6,620.  Againj 
under  a  force  of  1*61  tapping  changed  B  from  7,120  to 


14000 
12000 

10000 
B 

8000 

GOOO 
4000 
2000 

1-1  £  — 

.  —  —  — 

£=* 

—  <— 

—  = 

== 

=» 

!  

*~"~T 

.  —  y- 

{ 

i 

*  •» 

.3 

! 

I      Z 


3        4        5       6        7      8        9       10       II       12       13       (4       15      16     17 

Magnetising  Force    due    CO    Solenoid 


FIG.  56.— Magnetisation  of  Very  Soft  Annealed  Iron  Wire.    Effects  of 
tapping  shown  thus, . 

11,600,  and  under  a  force  of  3-4  it  changed  B  from  11,940  to 
12,960.  On  coming  down  the  effects  were  equally  well  marked. 
When  the  force  had  been  reduced  from  a  fairly  high  value  to 
0-33,  tapping  brought  B  down  from  11,260  to  6,880,  and 
finally  when  the  force  was  0  the  residual  value  of  B,  amounting 
to  6,880,  was  reduced  by  tapping  to  320.  The  forces  whose 
values  are  stated  here  are  those  due  to  the  solenoid  without 
allowing  for  the  reaction  of  the  specimen  itself  upon  the  mag- 
netising field.  The  complete  results  of  this  experiment  are 
shown  in  Fig.  56,  where  the  full  lines  show  those  parts  of  the 
process  which  were  performed  without  tapping;  and  the  changes 
Of  magnetic  state  brought  about  by  tapping,  while  the  external 
field  was  kept  constant,  are  shown  thus  : . 


118  MAGNETISM   IN   IRON. 

In  experiments  of  the  same  class  with  hard  iron  or  with  steel 
vibration  produces  effects  of  the  same  general  kind ;  but  its 
influence  in  destroying  hysteresis  is  far  less  complete  than  in 
soft  iron.  In  a  piece  of  iron  wire  of  the  same  quality  as  the 
last,  but  not  annealed,  where  a  residual  magnetism  (B)  amount- 
ing to  7,000  was  left  after  applying  a  force  of  17,  the  residue 
fell  to  2,500  when  the  specimen  was  smartly  tapped. 

Magnetic  hysteresis  exhibits  itself  in  other  changes  of  mag- 
netism as  well  as  in  the  changes  that  are  brought  about  by 
varying  the  magnetic  force.  It  is  a  prominent  feature  in  the 
effects  of  stress  upon  magnetic  quality,  but  the  consideration  of 
it  in  this  aspect  will  be  more  conveniently  reserved  for  a  later 
chapter. 


FIG.  56A. — Magnetic  Curve-Tracer. 

The  effects  of  temperature  on  hysteresis  will  be  referred 
to  in  Chapter  VIII. 

§  85a.  Magnetic  Curve-Tracer. — For  the  purpose  of  exhibit- 
ing the  behaviour  of  iron  or  steel  during  a  cyclic  process  of 
magnetisation,  the  author  has  devised  an  instrument  known  as 
the  magnetic  curve-tracer,*  which  causes  a  spot  of  light  to 
trace  upon  a  screen  the  form  assumed  by  the  B  H  curve  while  the 
iron  magnetising  process  is  actually  going  on.  By  making  the 
process  happen  fast  enough  the  movement  of  the  spot  of  light 
may  be  made  to  show  a  continuously  luminous  curve.  The 

*  See  The  Electrician,  May  26,  1893. 


MAGNETIC    CUE.VB   TRACER. 


119 


mirror  and  other  moving  parts  of  the  apparatus  are  sufficiently 
free   from   inertia  to  allow  a  cycle   of   magnetisation   to   bd 


QZD 


repeated  several  times  in  a  second.     The  mirror  receives  two 
components  of  angular  motion — a  vertical  component,  which  is 


120  MAGNETISM    IN   IRON. 

proportional  to  the  magnetisation  of  the  iron,  and  a  horizontal 
component,  which  is  proportional  to  the  magnetising  force. 
The  apparatus  is  shown  in  Fig.  56A,  but  its  working  will  be 
more  readily  understood  by  reference  to  Fig.  56s,  which  shows 
the  principal  parts  diagrammatically. 

E  is  the  mirror,  which  is  mounted  on  a  single  needle  point  in 
such  a  way  that  it  has  two  degrees  of  freedom  for  deflection. 


Fia.  56c. — Cyclic  process  of 

magnetisation  automatically  Fia.  56D. — Cyclic  Process  with  subordinate 
recorded  by  the  Magnetic  loops. 

Curve  Tracer. 

It  receives  azimuthal  movement,  causing  the  spot  of  light  to 
travel  horizontally  from  the  wire  B  B,  which  is  tightly  stretched 
in  a  narrow  gap  in  a  magnet  C,  and  is  connected  by  a  thread 
to  the  frame  which  carries  the  mirror.  The  magnet  C,  which  may 
conveniently  be  made  by  cutting  a  longitudinal  slot  in  a  piece  of 
iron  pipe,  is  magnetised  by  a  longitudinally  wound  coil,  through 
which  a  constant  current  passes.  The  lines  of  force  accordingly 
jump  across  the  slot  in  which  the  wire  B  B  is  strung,  forming  a 


MAGNETIC    CURVE    TRACER.  121 

constant  field  there.  The  variable  magnetising  current  which 
is  to  act  on  the  iron  under  examination  is  caused  to  pass 
through  the  wire  B  B,  and  hence  any  variation  in  the  current 
produces  corresponding  horizontal  movements  of  the  spot  of 
light  reflected  from  the  mirror.  At  the  same  time  the  mirror 
receives  vertical  movement  through  another  thread,  which 
connects  it  to  the  wire  A  A  stretched  in  a  gap  in  the  magnet 
under  examination.  This  magnet  is  made  up  of  two  rods  D  D 
connected  at  the  back  by  a  yoke,  and  terminating  in  pole  pieces, 
between  which  is  the  narrow  gap  containing  the  stretched 
wire  A  A.  A  constant  current  is  kept  up  in  the  wire  A  A,  and 
it  therefore  sags  up  or  down  proportionally  to  the  variations  of 
magnetism  in  the  rods  D  D.  These  rods  are  surrounded  by 


FIG.  56E. 

magnetising  coils,  and  the  current  which  magnetises  them 
passes  also  through  the  wire  B  B,  which,  as  has  just  been  said, 
is  stretched  in  a  constant  magnetic  field,  The  wire  B  B 
consequently  sags  out  or  in,  giving  horizontal  deflection  to  the 
mirror,  by  amounts  which  are  proportional  to  the  magnetising 
force  in  the  coils  of  D  D.  Hence,  to  describe  a  magnetising 
curve  for  the  rods  D  D  it  is  only  necessary  to  apply  a  gradually- 
increasing  current  to  the  coils  of  D  D,  when  the  mirror 
takes  vertical  movement  proportional  to  the  magnetism  and 
horizontal  movement  proportional  to  the  magnetising  force  ; 


122 


MAGNETISM    IN    IRON. 


and  by  reducing  the  current  to  zero,  re  applying  it,  reversing  It, 
and  so  on,  all  the  characteristics  of  the  magnetising  process  are 
rendered  obvious  at  a  glance. 

The  magnetising  current  must  be  varied  gradually,  not  by 
sudden  steps,  and  for  this  purpose  a  liquid  resistance  and 
liquid  commutator  are  useful. 

With  a  liquid  commutator  the  apparatus  may  readily  be 
arranged  so  that  a  complete  cycle  of  magnetisation — the  usual 
cycle  of  double  reversal — can  be  gone  through  in  one-tenth 
or  even  one-twentieth  of  a  second  ;  and  this  allows  the  spot 


56F.— Cyclic  Curves  in  Iron  and  Steel. 


of  light  to  trace  a  curve  which  appears  as  a  continuously 
luminous  line.  For  high-speed  working  such  as  this  the  metal 
of  the  magnetic  circuit  D  D  must  be  laminated.  For  some 
purposes,  however,  it  seems  best  to  trace  the  curve  more  slowly, 
following  with  a  pencil  the  movement  of  the  spot  of  light,  and 
so  obtaining  a  permanent  record,  or  recording  the  movement 
of  the  spot  on  a  photographic  plate. 

The  curves  shown  in  Figs.  56c  and  56D  are  reproduced  from 
photographs  of  magnetic  cycles  taken  by  means  of  this 
instrument,  using  a  sensitive  plate  to  record  the  movements  of 


MAGNETIC    CURVE    TRACER. 


123 


the  spot  of  light,  and  using  laminated  iron  as  the  material 
under  examination.  When  solid  rods  of  soft  iron  are  used  to 
form  the  magnet,  the  influence  of  time  in  the  performance  of 
the  cycle  becomes  very  marked.  In  that  case  even  a  com- 
paratively slow  increase  of  current  is  followed,  after  it  ceases, 
by  a  continued  creeping  up  of  the  magnetism,  and  the  spot  of 
light  goes  on  rising  for  some  seconds.  In  great  part,  at  least, 
this  effect  is  to  be  attributed  to  Foucault  currents  in  the  iron. 
It  follows  that  a  cyclic  process,  in  solid  rods,  takes  very 
different  forms  when  gone  through  at  different  rates.  Fig.  56E 
illustrates  this  by  giving  a  set  of  magnetic  curve-tracer  records 
for  a  pair  of  soft  iron  rods  Jin.  in  diameter.  The  curve  a  is 


Fia.  660 


obtained  by  going  very  slowly  round  the  cycle  and  shows  the 
hysteresis  loop  in  its  normal  state,  undisturbed  by  Foucault 
currents.  The  curves  b  and  c  show  how  much  disturbance  is 
produced  when  the  period  is  3  seconds  and  0-43  second 
respectively.*  Figs.  56p  and  56a  are  further  examples  of  curves 
given  by  the  magnetic  curve-tracer.  In  these  the  curve  is  traced 
by  going  slowly  round  the  cycle,  and  marking  successive  posi- 
tions reached  by  the  spot  of  light.  In  56o  the  magnetising 
current  was  progressively  raised  from  1  to  3  amperes. 

*  An  account  of  these  and  other  investigations  made  by  aid  of  the 
magnetic  curve  tracer  will  be  found  in  a  paper  by  MISR  Klaassen  and  the 
author  on  "The  Magnetic  Qualities  of  Iron,"  Phil.  Trans.,  1894,  p.  1024. 
In  this  connection  reference  should  be  made  to  a  research  by  J.  Hopldnson 
and  E.  Wilson  on  "  The  Propagation  of  Magnetisation  in  Iron  as  Affected 
by  the  Electric  Currents  in  the  Iron,"  Phil.  Trans.,  1895,  Vol.  186,  p.  93. 


CHAPTER  VI. 


MAGNETISM   IN   WEAK   FIELDS. 

§  86.  Permeability  with  respect  to  Small  Magnetic  Forces. 
— The  instances  which  have  been  set  forth  in  earlier  chapters 
may  suffice  to  give  a  general  notion  of  the  behaviour  of  iron 
and  the  other  magnetic  metals  when  exposed  to  magnetic  fields 
of  moderate  strength.  It  remains  to  give  some  account  of 
experiments  dealing  with  the  two  extremes  of  very  weak  and 
very  strong  magnetisation.  The  effects  of  weak  fields  will  be 
taken  up  first. 

A  glance  at  the  curves  of  B  and  H  or  of  I  and  H  for  any 
of  the  examples  which  have  been  already  given  will  serve  to 
show  that  the  initial  permeability — that  is  to  say,  the  per- 
meability at  the  beginning  of  the  process  of  magnetisation — is 
so  comparatively  small  that  special  means  are  required  to 
examine  its  value.  The  arrangements  for  measuring  this  early 
magnetism,  whether  they  are  ballistic  or  magnetometric,  must 
be  much  more  sensitive  than  those  that  serve  when  we  have 
to  deal  with  later  portions  of  the  curve.  So  small,  indeed, 
is  the  permeability  under  very  feeble  forces,  compared  with 
the  permeability  found  later,  that  without  special  appliances 
one  might  readily  fall  into  th3  error  of  supposing  it  to  be 
initially  zero.  Experiments  made  by  Baur,  Lord  Rayleigh, 
and  others  are  conclusive,  however,  in  showing  that  this  is  not 
the  case.  They  show  that  the  initial  permeability  has  a 
finite  value  which  is  applicable,  without  sensible  change, 
so  long  as  the  magnetising  force  remains  very  small.  In  other 
words,  the  magnetisation  curve  starts  with  a  definite  gradient, 
and  its  very  early  portion  is  nearly  straight.  Lord  Rayleigh  has 
carried  his  investigation  of  the  action  of  weak  forces  further, 


PERMEABILITY    UNDER    SMALL   MAGNETIC    FORCES. 


125 


showing  that  the  permeability  has  a  finite  value  with  respect 
to  any  small  cyclic  change  of  magnetic  force  when  that  is 
frequently  repeated,  whether  the  piece  be  otherwise  mag- 
netised or  not — a  value  which  is  sensibly  constant  when 
the  range  of  change  is  varied,  provided  the  range  be  kept  very 
small,  and  which  is  approximately  independent  of  the  mean 
condition  as  to  force  and  magnetisation,  provided  the  magnetic 
state  does  not  approach  saturation. 

Baur's  experiments  were  made  ballistically  with  a  ring  of 
soft  iron,  the  cross-section  of  which  had  a  diameter  of  a  little 
over  two  centimetres.  Reduced  to  C.-G.-S.  measure,  his  results 
for  one  trial  are  as  follows  : — * 


H 

1 

K 

0-0158 

0-263 

16-5 

0-0308 

0-547 

17-6 

0-0708 

7-633 

23-0 

0-1319 

3-815 

28-9 

0-230 

9-156 

39-8 

0-384 

22-487 

58-6 

When  these  values  of  the  susceptibility  K  are  plotted  in  rela- 
tion to  H,  they  are  seen  to  lie  on  what  is  practically  a  straight 
line.  By  producing  the  straight  line  backwards  to  cut  the 
axis,  the  value  of  K  corresponding  to  H  =  0  is  found  to  be  14'5. 
This  is,  therefore,  the  susceptibility  with  respect  to  indefinitely 
feeble  forces ;  the  corresponding  initial  permeability,  /z,  is  182. 
Moreover,  with  respect  to  forces  which  are  still  feeble  though 
not  indefinitely  small,  the  susceptibility  and  permeability  may 
be  expressed  by  the  equations 

/c  =  14-5  +  110  H,f 

ft=  183  + 1382  H, 

which  apply  with  much  accuracy  within  the  limits  of  H  used  In 
the  experiment.  With  any  considerably  higher  force,  however, 
these  formulas  would  not  apply.  It  follows  that  the  relation 

*  C.  Baur,  Inaugural  Dissertation,  Zurich,  1879.  Wied.  Annalen,  XI., 
1880,  p  399. 

t  Baur  gives  *=15  + 100  H,  but  the  constants  given  in  the  text  seem  to 
the  writer  to  agree  better  with  the  numerical  results  of  the  tests. 


126  MAGNETISM    IN    IRON. 

of  magnetisation  to  magnetic  force  for  feeble  forces  may  be 
expressed  thus : 

1  =  14-5  H  +  110  H2, 
B  =  183  H  + 1382  H2. 

These  particular  numerical  constants  are,  of  course,  to  be  taken 
as  applying  to  the  specimen  of  soft  iron  tested  by  Baur ;  but 
similar  parabolic  formulas  may  be  constructed  with  different 
constants  for  any  specimen  of  any  of  the  magnetic  metals.  In 
other  words,  the  curve  of  I  and  H  or  of  B  and  H  is  sensibly  a 
parabola  in  its  earliest  stages,  starting,  however,  with  a  finite 
inclination  to  the  axis  of  H.  For  excessively  feeble  forces  it 
is  virtually  an  inclined  straight  line,  the  term  involving  H2 
being  then  negligible. 

§  87.  Lord  Rayleigh's  Experiments. — The  inference  drawn 
by  Baur  as  to  the  value  of  K  when  H  is  zero  depends  on  the 
legitimacy  of  extending  the  straight  line  connecting  K  and  H 
backward  beyond  the  region  of  actual  experiment  to  cut  the 
axis  of  K.  It  has  been  entirely  confirmed  by  the  experiments 
of  Lord  Rayleigh,*  who  has  examined  the  action  of  much  feebler 
magnetic  forces,  and  has  found  that  the  proportionality  of  mag- 
netic induction  to  magnetic  force  continues  to  hold  good  when 
the  force  is  excessively  reduced. 

In  his  experiments  a  bar  or  wire  of  iron  was  tested  magneto- 
metrically  with  one  end  very  near  the  magnetometer,  and 
with  a  compensating  coil  adjusted  to  balance  the  magnetism 
which  a  feeble  magnetising  current  induced  in  the  bar.  The 
specimen  under  examination  being  a  piece  of  Swedish  iron  wire 
(not  annealed),  the  compensating  coil  was  adjusted  so  that 
there  was  no  movement  of  the  magnetometer  needle  when 
a  magnetising  current  was  made  or  broken,  the  strength 
being  such  as  to  give  a  field  of  0'04  C.-G.-S.  Then  the 
strength  of  the  current  was  gradually  reduced  till  the  mag- 
netic force  fell  to  about  0'00004,  and  it  was  found  that  the 
compensation  remained  perfect.  In  other  words,  within  these 
limits  the  induced  magnetism  was  proportional  to  the  inducing 
force  :  K  and  p  were  constant.  "  In  view  of  this,"  says  Lord 
Rayleigh,  "neither  theory  nor  observation  give  us  any  reason 

*  Phil.  Mag.,  March,  1887, 


MAGNETIC   VISCOSITY    UNDER    SMALL    FORCES.  127 

for  thinking  that  the  proportionality  would  fail  for  still  smaller 
forces."  Quite  similar  results  were  obtained  with  other  speci- 
mens of  unannealed  iron  and  of  steel.  The  range  through 
which  K  and  //,  are  sensibly  constant  is  much  less  in  annealed 
than  in  hard  iron.  Within  this  range  of  force  there  is  no  re- 
tentiveness  -,  the  magnetising  process  begins  like  the  straining 
of  a  solid  body  with  an  elastic  stage  within  which  there  is  no 
"  permanent  set."  When  the  magnetising  force  was  increased 
above  0-04  the  compensation  failed  to  remain  exact,  and  the 
deviations  followed  the  parabolic  law  stated  above.  The  formulas 


agreed  well  with  the  results  of  experiment  for  values  of  H 
ranging  up  to  1*2  C.-G.-S.  unit.  (In  comparing  these  with  the 
formulas  given  in  the  last  paragraph,  it  must  be  remembered 
that  these  refer  to  hard  iron,  the  others  to  annealed  iron  :  the 
initial  susceptibility  is  less  here,  and  the  deviation  from  the 
initial  value  is  very  much  less  rapid.)  With  another  specimen 
of  hard-drawn  iron  wire  the  initial  value  of  p  was  87. 

Lord  Kayleigh  has  also  examined  the  effect  of  alternately 
applying  and  removing  a  small  amount  of  magnetic  force,  when 
the  piece  is  kept  more  or  less  strongly  magnetised  by  means  of 
a  constant  force.  So  long  as  the  constant  force  is  moderately 
small,  and  the  mean  magnetisation  consequently  not  very 
strong,  the  susceptibility  with  regard  to  alternate  applications 
and  removals  of  a  small  part  of  the  force  is  not  materially 
different  from  the  initial  susceptibility  of  the  same  piece  when 
unmagnetised.  But  as  the  mean  magnetisation  is  raised,  the 
susceptibility  with  respect  to  small  changes  of  force  becomes 
reduced.  In  a  piece  of  hard  iron  a  steady  force  of  29  C.-G.-S. 
had  the  effect  of  reducing  the  susceptibility  with  respect  to 
small  alternations  by  about  40  per  cent,  of  its  original  value  \ 
and  in  a  piece  of  annealed  iron  the  reduction  due  to  the  same 
steady  force  was  more  than  80  per  cent. 

§  88.  Magnetic  Viscosity  under  Small  Forces.  —  Allusion 
has  already  been  made  (§  50)  to  the  fact  that  after  any  change 
has  taken  place  in  the  magnetic  force  acting  on  a  piece  of  soft 
annealed  wrought  iron,  some  time  elapses  before  the  correspond- 


128  MAGNETISM    IN   IRON. 

ing  change  of  magnetic  state  is  complete.*  This  magnetic 
viscosity  is  most  noticeable  when  we  have  to  deal  with  feeble 
forces  or  with  small  changes  of  force,  and  when  the  specimens 
tested  are  of  considerable  size.  In  such  cases  the  time-lag  in 
magnetisation  may  be  so  great  that  the  ballistic  method,  which, 
of  course,  omits  to  take  note  of  slow  continuous  changes,  is  not 
properly  applicable. 

In  describing  the  experiments  which  were  referred  to  in  the  last 
paragraph,  Lord  Eayleigh  remarked  that  when  small  magnetic 
forces  were  applied  to  hard  iron  or  steel  it  was  possible  to  adjust 
the  compensating  coil,  so  that  neither  at  the  moment  of  closing 
the  magnetising  circuit  nor  afterward  was  there  any  deflection — 
which  means  that,  so  far  as  the  magnetometer  can  decide,  these 
metals  take  their  full  magnetism  at  once.  With  annealed  wrought 
iron,  however,  the  effects  were  more  complicated.  "When  the  coil 
was  so  placed  as  to  reduce  as  much  as  possible  the  instantaneous 
effect,  there  ensued  a  drift  of  the  magnetometer  needle  in  such 
a  direction  as  to  indicate  a  continued  increase  of  magnetisation. 
Precisely  opposite  effects  followed  the  withdrawal  of  the 
magnetising  force.  The  settling  down  of  the  iron  into  a  ne\? 
magnetic  state  is  thus  shown  to  be  far  from  instantaneous." 

Following  Lord  Rayleigh's  plan  of  balancing  the  instantaneous 
effect  by  means  of  a  compensating  coil,  and  then  observing  the 
drift,  the  writer  examined  this  time-lag  in  the  magnetisation  of 
a  thick  wire  of  annealed  wrought-iron  0*404  cm.  in  diameter 
and  39*6  cms.  long.f  The  wire  was  demagnetised  by  reversals 
to  begin  with,  and  feeble  magnetising  forces  were  used,  not  at 
first  exceeding  O'l  C.-G.-S.  So  long  as  the  force  was  less  than 
this  it  was  found  that  one  adjustment  of  the  compensating  coil 
served  to  balance  the  instantaneous  effect  of  making  or  break- 
ing or  reversing  the  current.  When  the  compensation  was 
correct  the  magnetometer  needle  began  to  drift  slowly  over  as 
soon  as  the  magnetising  force  was  either  applied  or  removed ;  and 

*  Phil.  Trans.,  1885,  p.  569. — "  When  the  magnetising  current  was  applied 
to  long  wires  of  soft  iron,  either  gradually  or  with  more  or  less  sudden 
ness,  there  was  a  distinct  creeping  up  of  the  magnetometer  deflection  after 
the  current  had  attained  a  steady  value.  This  action  was  sometimes  so 
considerable  as  to  oblige  me  to  wait  for  some  minutes  before  taking  the 
magnetometer  reading." 

t  Proc.  Roy.  Soc.,  June  20,  1889. 


MAGNETIC   VISCOSITY   UNDER   SMALL   FORCES. 


129 


by  observing  the  drift  and  adding  that  to  the  amount  neutralised 
by  the  compensating  coil,  the  total  magnetism  after  any  time 
was  readily  deduced.  A  force  of  0-044  C.-G.-S.  was  applied,  the 
instantaneous  effect  of  which  was  to  produce  a  value  of  I  equal 
to  0'44  ;  in  five  seconds  this  crept  up  to  0'58,  and  in  60  seconds 
to  0'67.  Then  the  magnetising  current  was  broken ;  the  instan- 
taneous effect  on  I  was  to  remove  0'44,  leaving  0*27 ;  in  five 
seconds  this  residue  fell  to  0-09,  and  before  60  seconds  it  had 
completely  disappeared.  Next  a  magnetising  force  of  0'084  was 
applied.  The  value  of  I  reached  at  once  was  0'85 ;  in  five 
seconds  it  crept  up  to  1-20,  and  in  60  seconds  to  1-40.  On 
breaking  the  current,  I  fell  at  once  to  0'55,  after  five  seconds  to 


005  ' 

Force  H. 


FIQ.  57. 

0'23,  and  after  60  seconds  to  0*07.  Possibly  this  small  residue, 
or  part  of  it,  was  permanent.  These  results  are  shown  in  Fig. 
57.  Precisely  similar  results  were  obtained  by  reversing  feeble 
magnetic  forces,  the  initial  gradient  of  the  lines  being  the 
same  when  the  force  was  reversed  as  when  it  was  applied  and 
removed.  If  we  measure  the  initial  susceptibility  by  the  imme- 
diate effect  of  applying  or  reversing  H  it  is  10  ;  if  we  measure 
it  by  the  effect  after  one  minute  it  is  about  15. 

Fig.  58  shows  the  results  of  another  experiment,  in  which 
successive  forces  were  applied,  ranging  up  to  about  0*34  C.-G.-S., 
the  compensating  coil  being  adjusted  for  each  force  to  give  an 
instantaneous  balance,  so  that  the  effect  of  the  subsequent 
creeping  up  might  be  observed.  Before  applying  each  force  the 
specimen  was  completely  demagnetised.  The  three  curves, 


130 


MAGNETISM   IN   IRON. 


Fig.  58,  show  the  amounts  of  magnetism  taken  (a)  at  once, 
(6)  after  five  seconds,  and  (c)  after  one  minute.     In  noting  the 


y 


<7 
.1 


Magnetising  Force  H. 
FIG.  58. — Effects  of  applying  Feeble  Magnetising  Forces  to  a  Soft  Iron  Rod. 


•081 


20  40 

Time  in  Seconds . 


60 


Fia.  59.— Growth  of  Magnetism  after  applying  Feeble  Magnetising  Forces. 

gradual  growth  of  magnetism  after  each  force  was  applied, 
readings  of  the  magnetometer  were  taken  every  five  seconds, 


TIME-LAO    IN    MAGNETISATION. 


131 


and  the  two  curves  of  Fig.  59  have  been  drawn  from  these,  to 
show  the  time  rate  at  which  the  process  of  creeping  up  went 
on  under  the  action  of  magnetising  torces  equal  to  0'035  and 
0*081  respectively. 

§  89.  Further  Experiments  on  Time-Lag  in  Magnetisation. 
Similar  differences  between  the  immediate  and  ultimate  action 
of  magnetic  force  on  soft  iron  present  themselves  when  we 
examine  the  effects  of  small  increments  of  the  magnetic  force 
at  any  stage  in  the  process  of  magnetisation.  In  another  ex- 
periment, which  was  made  with  the  same  specimen  of  annealed 


0'4  tr5 

Magnetising  force  H. 
Fia.  60.—  Effects  of  Steps  in  the  Magnetisation  of  a  Soft  Iron  Rod. 

wrought  iron,  the  magnetising  force  was  applied  in  a  series  of 
small  steps  —  each  step  being  produced  by  a  rapid  but  not  quite 
sudden  augmentation  of  the  magnetising  current.  The  imme- 
diate effect  of  each  step  was  balanced  by  means  of  the  compen- 
sating coil,  and  after  each  step  a  pause  of  one  minute  was 
made  during  which  the  gradual  growth  of  magnetism  was 
observed.  The  results  are  shown  in  the  full  lines  of  Fig.  60  ; 
the  dotted  line  has  been  added  to  show  that  the  points  reached 
after  the  pauses  of  one  minute  lie  in  a  continuous  curve.  As 
the  experiment  was  continued  into  higher  parts  of  the  magne- 
tisation curve,  the  compensating  coil  had  to  be  pushed  a  little 

K2 


OF  THE 

UNIVERSITY 


132 


MAGNETISM    IN   IRON. 


nearer  the  magnetometer  to  procure  a  perfect  balance :  in 
other  words,  the  immediate  effect  of  the  step  became  somewhat 

greater.     At  the  beginning,   the  instantaneous  value  of  —I 

d  H 

was  about  10;  but  when  the  experiment  of  Fig.  60  was  ex 
tended  until  the  force  produced  by  the  magnetising  solenoid 
was  3  C.-G.-S.  or  so,  and  I  was  about  320,  the  instantaneous 

value  of  — —  rose  to  13.     In  that  region  of  the  curve,  the 
d  H 

creeping-up  of  magnetism  after  a  very  small  step-up  of  the  cur- 
rent was  enormous ;  in  the  course  of  one  minute  it  amounted 


1. 


H. 

Fid.  61. — Effects  of  a  sudden  small  increase  of  Force  in  the  steep  part  of 
the  Magnetisation  Curve. 

to  six  or  seven  times  the  immediate  effect  of  the  step.  Fig.  61 
illustrates  the  kind  of  action  which  is  observed  when  a  small 
increment  of  magnetising  force  is  made  to  take  place  quickly 
after  a  pause  anywhere  in  the  steep  part  of  the  magnetising 
process,  the  metal  dealt  with  being  soft  wrought  iron.  The 
dotted  line  is  the  normal  slope  of  the  magnetisation  curve 
when  the  process  of  magnetising  is  performed  slowly.  A 
very  small  increment  of  H  rapidly  performed  after  a  pause  at 
P  produces  an  immediate  effect,  P  Q,  which  is  followed  by  the 
slow  creeping  up  Q  R.  It  is  only  when  the  step  is  a  very 
small  one  that  P  Q  correctly  represents  the  immediate 
effect, 


TIME-LAG   IN    MAGNETISATION.  133 

Very  Interesting  results  are  obtained  in  examining  how  the 
time-rate  of  creeping  up  after  a  step  is  affected  by  the  length 
of  the  pause  (under  constant  force)  which  preceded  the  step. 
When  the  preceding  pause  is  long  the  creeping  up  which  fol- 
lows a  step  goes  on  much  more  slowly  than  when  the  preceding 
pause  is  short.*  In  an  experiment  with  the  same  specimen  of 
soft  iron  the  effects  of  two  equal  small  steps  were  compared, 
both  made  at  the  same  part  of  the  magnetisation  curve, 
one  after  the  magnetising  force  had  been  kept  constant  for 
three  minutes,  and  the  other  after  it  had  been  kept  constant 
for  an  hour.  The  immediate  effects  were  the  same ;  but  the 
subsequent  creeping  up,  which  was  observed  during  no  less 
than  ten  minutes,  went  on  so  much  faster  in  the  former  case 
that  it  amounted  in  ten  minutes  to  531  scale  divisions 
of  the  magnetometer,  as  against  320  scale  divisions  in  the 
latter. 


The  effects  of  an  alternate  small  step  up  and  step  down,  per- 
formed at  any  stage  in  the  process  of  magnetisation,  are  quite 
like  those  that  have  been  shown  in  Fig.  57.  After  the  steps 
have  been  repeated  often  enough  to  bring  about  a  cyclic 

set  of  changes,  the  instantaneous  value  of  -TYI  becomes  ap- 

d  M 

proximately  the  same  as  at  the  initial  part  of  the  curve — 
namely,  about  10  in  the  particular  specimen  examined — unless 
the  whole  magnetisation  approaches  saturation,  in  which  case 

the  value   of  — —  is  distinctly  less.    The  diagram  (Fig.  62)  re- 
d  H 

presents  in  a  general  way  the  change  of  magnetism  which  takes 
place  when  any  very  small  periodic  variation  of  magnetic  con- 
dition is  made  to  occur  in  a  soft  iron  bar,  about  a  mean  condi- 

*loc.  cit.,  p.  280. 


134  MAGNETISM    IN    IRON. 

tion  0.  If  the  changes  of  force  occur  fast  and  without  pauses 
the  cycle  is  shown  by  the  lines  a  a'  and  a'  a.  They  enclose  no 
area,  and  there  is  no  dissipation  of  energy.  If,  on  the  other 
hand,  the  changes  of  force  occur  gradually  and  very  slowly  the 
cycle  is  shown  by  the  lines  c  c'  and  c'  c.  They  also  enclose  no 
area ;  and  again  there  is  no  dissipation  of  energy.  But  if  the 
changes  of  force  take  place  quickly,  with  pauses  at  the  extreme 
values,  the  cycle  is  b'  c'  b  c,  and  an  amount  of  energy  is  dissi- 
pated  which  is  to  be  measured  by  the  area  of  that  parallelo< 
gram.  In  most  actual  cases  in  which  the  force  varies  periodically 
it  does  so  not  suddenly  with  pauses  at  the  extreme  values,  but 
in  such  a  manner  that  a  loop  will  be  formed  instead  of  the 
parallelogram.  When  the  frequency  of  the  alternations  is  very 
great,  the  loop  will  flatten  itself  into  the  straight  line  a  a' ; 
when  the  frequency  is  very  small  it  will  again  flatten  itself 
into  the  straight  line  b  b'.  With  any  frequency  lying  between 
these  extremes  there  will  be  dissipation  of  energy,  and 
when  the  limits  and  mode  of  variation  of  the  force  ara 
specified,  there  must  be  some  particular  frequency  which 
will  make  the  amount  of  energy  dissipated  in  the  cycle  a 
maximum. 

In  hard  iron  and  in  steel  the  phenomenon  of  time-lag  in  mag- 
netisation occurs,  but  so  slightly  as  to  be  scarcely  observable.  A 
piece  of  the  same  wire  as  had  been  used  in  the  above  experi- 
ments was  hardened,  after  being  annealed,  by  stretching  it  a 
little  beyond  the  limit  of  elasticity.  Scarcely  a  trace  of  creeping 
could  be  detected  when  a  feeble  magnetic  force  was  applied 
to  the  wire  in  this  hardened  state,  but  it  was  possible  to  pro- 
duce a  measurable  amount  of  creeping  by  first  applying  a 
moderately  strong  magnetising  force,  and  then  making  a  small 
step  up  after  a  pause.  The  initial  instantaneous  value  of 

. for  a  small  step  was  5  3. 

d  H 

The  whole  phenomenon  depends  much  on  the  size  of  the 
specimen  that  is  tested.  In  the  experiments  which  have  been 
described  the  iron  was  a  rod  four  millimetres  in  diameter. 
Smaller  rods  showed  much  less  magnetic  "  creeping,"  and  when 
a  bundle  of  fine  annealed  iron  wire  was  substituted  for  the  rod, 
nearly  all  trace  of  creeping  disappeared.  The  cause  of  this 
difference  is  at  present  obscure. 


MOLECULAR    ACCOMMODATION.  135 

§  90.  Molecular  Accommodation.  —  Closely  related  to  the 
experiments  which  have  been  detailed  in  this  chapter  are 
results  recently  published  by  H.  Tomlinson.*  Examining  the 
action  of  feeble  magnetic  forces,  in  the  region  within  which  the 
relation  of  B  to  H  may  be  expressed  (§  86)  in  the  form. 


he  has  discussed  the  influence  of  temperature  and  other  con- 
ditions on  the  constants  a  and  b.  The  constant  a  is  of  course 
the  initial  permeability,  and  it  is  on  the  value  of  b  that  the 
dissipation  of  energy  depends.  Some  of  the  more  interesting 
of  Tomlinson's  results  may  be  briefly  stated  in  his  own 
words  :  — 

"  The  internal  friction  of  iron,  nickel,  and  cobalt  in  any  com- 
plete cycle  may  be  decreased  by  repetition  of  the  cycle  ;  the 
molecules  are  said  to  be  '  accommodated  '  by  this  process. 

"  The  molecular  '  accommodation  '  of  freshly  annealed  iron 
can  be  largely  aided  by  repeatedly  raising  the  metal  to  100°C  , 
and  then  allowing  it  to  cool. 

"  The  '  accommodation  '  of  the  molecules  of  iron,  nickel,  and 
cobalt  is  disturbed  by  very  slight  mechanical  shocks,  by  small 
change  of  temperature,  or  by  magnetisation  beyond  certain 
limits  ;  under  such  influences  the  internal  friction  may  for  a 
time,  or  even  permanently,  be  considerably  increased. 

"  The  values  of  a  and  b  for  iron  are  temporarily  increased 
when  the  temperature  is  raised  from  0°C.  to  100°C." 

*  Proc.  Roy.  Soc.  Dec.  5,  1889. 


CHAPTER  VII. 


MAGNETISM  IN  STRONG  FIELDS. 

£  91.  Magnetisation  in  Strong  Fields. — We  pass  now  to  speak 
of  the  opposite  extreme  of  the  magnetising  process.  In  study- 
ing the  relation  of  magnetism  to  magnetising  force  by  any  of 
the  methods  which  have  been  described  in  earlier  chapters,  it 
is  scarcely  practicable  to  raise  the  force  H  beyond  a  few  hun- 
dreds of  C.-G.-S.  units  at  the  most.  Formidable  difficulties 
present  themselves,  one  of  which  is  the  heating  effect  of  the 
magnetising  coil.  Special  methods  have  therefore  to  be 
resorted  to  when  we  wish  to  examine  the  behaviour  of  iron 
or  other  magnetic  metal  in  very  strong  fields. 

It  is  true  that  the  most  important  parts  of  the  magnetising 
process  lie  within  the  range  of  those  forces  which  may  easily  be 
produced  by  means  of  a  magnetising  coil.  Within  that  range 
the  permeability  or  the  susceptibility  passes  through  its  great 
changes,  increasing  quickly  from  a  small  finite  initial  value  to 
a  maximum  ten  or  fifteen  times  as  great,  and  decreasing  almost 
as  quickly  to  a  value  smaller  than  the  first.  Within  that 
range,  too,  the  residual  magnetism  apparently  reaches  the  full 
value  it  is  capable  of  reaching.  It  is  within  that  range  that 
the  most  prominent  features  in  the  influence  of  vibration,  of 
temperature,  and  of  stress,  manifest  themselves.  And  it  is  pro- 
bably true  that  whatever  knowledge  of  magnetic  quality  is 
wanted  for  application  to  the  practical  ends  of  electrical  engi- 
neering can  be  obtained  by  experiments  within  that  range. 

But  still  the  action  of  stronger  fields  is  of  very  great  interest, 
especially  in  relation  to  the  molecular  theory  of  magnetism  pro- 
pounded by  Weber.  According  to  Weber's  theory  the  molecules 
of  iron  or  any  other  magnetisable  metal  are  always  magnets. 
These  point  anyhow  in  the  unmagnetised  piece,  so  that  the 
sum  of  their  moments,  resolved  in  any  direction,  amounts  to 
eero,  and  the  piece,  therefore,  has  no  magnetism  as  a  whole. 
But  when  a  magnetising  force  acts  the  molecular  magnets  tend 


MAGNETISATION   IN   STRONG   FIELDS.  137 

to  turn  so  that  their  axes  may  point  more  nearly  in  the  direcv  ion 
in  which  the  force  acte;  and  thus  the  piece,  as  a  whole,  becon»«s 
a  magnet.  The  intensity  of  magnetisation  I  is  the  sum  (per  um\ 
of  volume)  tit  the  moments  of  the  molecular  magnets  resolved 
in  the  direction  of  the  magnetising  force.  We  shall  discuss  this 
theory  more  fully  in  a  later  chapter.  Meanwhile,  one  obvious 
deduction  from  it  may  be  pointed  out.  When  all  the  molecular 
magnets  are  turned  round  to  face  exactly  in  the  direction  in 
which  the  force  acts,  no  further  magnetisation  in  that  direction 
will  be  possible,  however  much  the  force  may  be  increased.  In 
other  words,  the  theory  points  to  this — that  the  intensity  of  mag- 
netisation I  has  a  saturation  value  which  cannot  be  exceeded, 
though  it  points  to  no  limit  to  the  value  which  B,  the  magnetic 
induction,  may  reach. 

In  experiments  made  with  moderately  strong  magnetising 
forces  both  B  and  I  are  increasing  slowly  at  the  last ;  and  it  is 
impossible  to  infer,  from  the  results  of  such  experiments, 
whether  B  or  I  or  either  of  them  is  approaching  a  finite  limit. 
The  curves  of  permeability  or  of  susceptibility  in  relation  to 
B  or  to  I  (such  as  have  been  given  in  Figs.  40,  41,  and  42)  do 
not  help  us  to  a  conclusion ;  we  cannot  produce  a  curve  of 
this  kind  beyond  the  region  of  experiment  until  it  cuts  the  axis 
of  B  or  of  I,  because  (as  Figs.  41  and  42  show)  the  curve 
bends  out  when  the  magnetising  force  is  sufficiently  increased. 
This  characteristic  of  the  curve  of  K  and  I  or  of  /x  and  B  was 
first  pointed  out  by  Fromme,*  and  has  been  commented  on  by 
a  number  of  other  experimenters.  In  some  of  the  writer's  ex- 
periments it  appeared  when  B  exceeded  about  15,000.1  Figures 
given  by  Bosanquet|  for  experiments  with  iron  and  steel  rings, 
in  one  of  which  the  induction  was  pushed  as  high  as  19,300, 
show  when  plotted  a  similar  inflexion  in  the  curve  of  p.  and  B, 
occurring  when  B  is  about  15,000.  The  same  feature  is  well 
shown  in  Fig.  63,  which  is  copied  from  a  Paper  by  Bidwell,§ 
describing  experiments  with  soft  wrought  iron,  in  which  the 

*  Fromme,  Gott.  Nahr.,  1875,  p.  500.  Wied.  Ann.  XIII.,  p.  695,  1881 ; 
see  also  J.  Haubner,  Wien.  Am.,  October  21,  1880 ;  Wied.  Beiblatter,  V., 
1881,  p.  205. 

t  Phil.  Trans.,  1885,  Part  II.,  p.  567. 

$  Bosanquet,  Phil.  Mag.,  February  and  May,  1885. 

§  Bidwell,Proc.  Roy.  Soc.,  Vol.  XL.,  1886,  p.  486. 


138 


MAGNETISM    IN    IRON. 


induction  was  raised  to  19,820,  with  the  result  of  reducing  /A  to 
33-9.  To  produce  this  the  force  H  was  585,  and  the  resulting 
magnetisation  I  was  1,530.  These  numbers  give  some  idea  of 
the  extent  to  which  experience  has  shown  it  is  practicable  to 
go  in  experiments  of  the  ordinary  class,  using  the  magnetising 

2,000 


1,000 


5,000 


10,000 
B 


15,000 


20,000 


Fio.  63. — Permeability  of  Wrought  Iron  when  Strongly  Magnetised. 

force  of  a  current  in  a  coil.*  To  answer  the  question  whether 
there  is  any  finite  limit  to  I  or  to  B,  we  have  to  go  far  beyond 
this  range. 

§  92.  The  Isthmus  Method. — This  name  has  been  given  to 
a  method  introduced  in  1887  by  the  writer  and  Mr.  W.  Low,t 
which  has  allowed  the  magnetisation  of  iron  to  be  raised  to 
greatly  higher  values,  with  the  result  of  showing  that,  while 
B  has  apparently  no  limit,  there  is  a  finite  limit  to  I,  as 
Weber's  molecular  theory  predicts. 

In  the  air-space  between  the  pole-pieces  of  a  strong  electro- 
magnet, we  have  a  magnetic  field  of  much  greater  intensity 
than  any  that  can  easily  be  produced  by  the  direct  action  of 
the  electric  current.  If  a  small  test-piece  of  the  metal  which 
is  to  be  magnetised  be  placed  across  this  space,  so  that  it 
forms  an  isthmus  between  the  two  pole-pieces,  it  will  become 
strongly  magnetised.  In  becoming  magnetised,  however,  it 
disturbs  this  field,  and  the  force  acting  on  it  may  be  very 

*  In  recent  experiments  by  du  Bois,  described  in  §  107  infra,  a  coil  was 
used  to  produce  magnetic  forces  which  ranged  up  to  1,300  C.-G.-S. 
tProc.  Roy.  Soc.,  March  24,  1887;  Phil.  Trans.,  1889,  A,  p.  221. 


THE   ISTHMUS   METHOD.  139 

different  from  the  force  which  existed  in  the  empty  space.  If 
it  is  a  short  cylinder  extending  lengthways  from  pole-piece  to 
pole-piece,  its  magnetism  will  be  very  unequal.  At  the  ends 
the  induction  will  have  the  same  value  as  it  has  in  the  pole- 
pieces  themselves ;  at  the  middle  it  will  be  stronger,  owing  to 
the  convergence  of  lines  of  induction  from  neighbouring  parts 
of  the  pole-pieces,  which  find  their  way  into  the  test-piece 
through  its  sides.  Evidently  we  may  increase  the  induc- 
tion in  the  middle  by  furnishing  the  specimen  with  spreading 
ends,  which  will  present  an  easier  path  along  which  the  lines  of 
induction  may  converge.  Moreover,  when  the  test-piece  takes 
the  form  of  a  bobbin,  with  a  short,  narrow,  central  neck, 
from  each  end  of  which  a  cone  extends,  spreading  over  the  face 
of  the  pole-piece,  it  becomes  possible  (by  giving  a  proper  form 
to  the  cone)  to  secure  that  the  central  neck  will  be  uniformly 
magnetised,  and  that  the  magnetic  force  which  acts  on  it  will 
have  the  same  value  as  the  magnetic  force  in  the  immediately 
surrounding  air-space.  The  magnetic  force  and  the  magnetic 
induction  within  the  neck  then  admit  of  being  measured,  and 
the  permeability,  susceptibility,  and  intensity  of  magnetisation 
under  exceedingly  strong  forces  are  readily  deduced. 

§  93.  Early  Experiments,  using  the  Isthmus  Method. — 
Figs.  64  and  65  show  two  forms  of  bobbin  which  were  used  in 
the  first  application  of  the  isthmus  method.  The  dimensions 
are  marked  in  millimetres.  The  central  neck  was  wound  with 
an  induction  coil  consisting  of  a  single  layer  of  fine  wire, 
and  its  magnetism  was  measured  by  the  ballistic  method. 
With  bobbins  of  the  shape  shown  in  Fig.  64,  the  induction  was 
measured  by  suddenly  slipping  the  bobbin  out  from  its  place 
between  the  pole  pieces  while  the  electro-magnet  was  excited.  An 
objection  to  this  is  that  it  takes  no  direct  account  of  the  resi- 
dual induction ;  it  shows  only  the  magnetism  that  is  lost  when 
the  bobbin  is  withdrawn  from  the  field.  The  residue  is  small, 
and  it  may  be  separately  measured  and  allowed  for ;  but  a 
better  arrangement  is  shown  in  Fig.  65,  where  the  bobbin  may 
be  turned  suddenly  round  so  that  its  magnetism  is  reversed  ; 
half  the  ballistic  effect  of  this  reversal  of  course  measures  the 
magnetic  induction.  To  measure  the  field  in  the  air-space 
immediately  surrounding  the  neck,  a  second  induction  coil  was 


140 


MAGNETISM    IN    IRON. 


wound  over  the  first,  but  at  a  little  distance  from  it,  so  that  a 
narrow  ring  of  non-magnetic  space — about  l'3mm.  wide — was 


FIG.  64. 


FIG.  65. 


included  between  the  two.     The  magnetic  force  in  this  space 
was  calculated  from  the  observed  difference  in  the  ballistic 


O'HH!   ISTHMUS   METHOD. 


effects  of  the  inner  and  outer  coil.  The  knowledge  of  it  allowed 
a  proper  correction  to  be  made,  by  which  the  whole  induction 
within  the  inner  coil  was  reduced  to  allow  for  those  lines  of  in- 
duction which  lay  within  it  but  not  within  the  iron. 

With  the  bobbins  shown  in  Figs.  64  and  65  the  outside  field 
— that  is  to  say,  the  magnetic  force  in  this  narrow  ring  of  space 
surrounding  the  neck — was  probably  a  very  little  stronger  than 
the  mean  force  within  the  metal  of  the  neck  itself.  Still,  the 
outside  field  was  so  nearly  equal  to  H  that  the  quantity 


B  —  outside   field 


approximated  closely  to  the  value  of  I,  and 


the  quantity. 


B 


approximated  closely  to  the  value  of 


outside  field 
the  permeability,  p. 

The  results  in  Table  VIII.  were  obtained  with  a  bobbin  of 
soft  Swedish  wrought  iron  in  the  annealed  state. 

TABLE  VIII.— Swedish  Wrought  Iron  in  Strong  Fields. 


Outside  field 
(=H  nearly). 

B 

B  -  outside  field 

B 

47T 

(=1  nearly). 

outside  field 
(=  A*  nearly). 

6,690 

27,960 

1700 

418 

8,900 

29,730 

1660 

334 

9,510 

30,820 

1700 

3-24 

10,000 

31,210 

1690 

312 

10,360 

31,630 

1700 

305 

10,810 

31,720 

1670 

2-94 

10,880 

32,060 

1690 

295 

11,200 

32,360 

1690 

2-90 

These  figures  show  that  in  the  very  strong  fields  with  which 
this  experiment  deals,  the  quantity  in  the  third  column,  which  is 
approximately  equal  to  the  intensity  of  magnetisation  I,  becomes 
practically  constant.  Such  variations  as  occur  in  the  numbers 
are  irregular  and  come  from  errors  of  observation.  The  iron  is 
here  in  a  condition  of  true  saturation ;  I  has  reached  a  value 
which  refuses  to  undergo  any  sensible  increase,  though  the 
strength  of  the  field  be  doubled;  but  the  field  itself  may  be 
increased  without  limit,  and  consequently  there  is  no  sign  of 
any  limit  to  the  value  of  B. 


142 


MAGNETISM   IN    IRON. 


Table  IX.  gives  the  results  of  a  similar  experiment  made 
with  a  bobbin  of  annealed  Lowmoor  wrought  iron,  and  with  a 
wider  range  of  magnetic  forces.  The  apparent  decrease  of  I  in 

TABLE  IX. — Lowmoor  Wrought  Iron  in  Strong  Fields. 


Outside  field 

B  -  outside  field 

B 

(  =  H  nearly). 

B 

47T 

(  =  1  nearly). 

outside  field 
(=/x  nearly). 

3,630 

24,700 

1680 

6-80 

6,680 

27,610 

1670 

4-13 

7,800 

28,870 

1680 

370 

8,810 

29,350 

1630 

3-33 

9,500 

30,200 

1650 

3-18 

9,780 

30,680 

1660 

314 

10,360 

30,830 

1630 

2-98 

10,840 

31,370 

1630 

2-89 

11,180 

31,560 

1620 

2-82 

TABLE  X. — Cast  Iron  in  Strong  Fields. 


Outside  field 
(  =  H  nearly). 

B 

B  =  outside  field 

B 

ATT 
(=1  nearly). 

outside  field 
(=  /A  nearly). 

3,900 

19,660 

1250 

5-04 

6,400 

21,930 

1240 

3-42 

7,710 

22,830 

1200 

2-96 

8,080 

23,520 

1230 

2-91 

9,210 

24,580 

1220 

2-67 

9,700 

24,900 

1210 

2-57 

10,610 

25,600 

1190 

2-46 

the  strongest  field,  which  is  shown  by  the  last  numbers  in  the 
third  column,  is  due  to  the  fact  that  the  outside  field  was  rather 
greater  tha  i  the  true  magnetic  force  within  the  metal.  When 
the  bobbin  is  so  shaped  that  this  source  of  error  is  avoided,  the 
apparent  decrease  disappears,  and  I  is  then  found  to  be  as  nearly 
constant  as  casual  errors  of  observation  allow  it  to  be. 

A  noticeable  feature  in  these  results  is  the  reduction  of  the 
permeability  that  is  brought  about  by  continuing  to  increase  the 
magnetising  force  after  a  state  of  saturation  has  been  reached. 
With  wrought  iron  such  as  was  used  here  the  initial  value 
of  /A  for  exceedingly  small  forces  is  nearly  200  j  and  the  maxi- 


THE    ISTHMUS    METHOD. 


143 


mum  of  /i,  reached  generally  with  a  magnetising  force  of  two  or 
three  units,  may  be  as  much  as  3,000.  Here,  with  a  magnetis- 
ing force  of  10,000  units  or  so,  p  has  fallen  to  less  than  3. 

Table  X.  gives  the  results  of  a  similar  experiment  with  cast 
iron.  In  it,  as  in  the  two  last  cases,  saturation  has  been 
reached  even  with  the  lowest  value  of  H  within  the  range  of 
the  observations.  The  saturation  value  of  I  in  this  cast  iron  is 
about  1,240 — a  value  distinctly  less  than  that  found  in  wrought 
iron.  Fig.  66  exhibits  in  the  form  of  curves  of  permeability 
the  results  given  in  Tables  IX.  and  X.  These  are  in  effect  an 


8    2 
O 
•I- 
CD  1 


* 


a    * 


B 


FIG.  66.  —  Curves  of  Permeability  for  Wrought  Iron  and  Cast  Iron  very 
Strongly  Magnetised. 

extension  into  regions  of  strong  force  of  curves  of  the  type 
shown  before  in  Figs.  41  and  42  and  in  Fig.  63. 

§  94.  Later  Experiments,  using  the  Isthmus  Method.  —  In 
subsequent  experiments*  the  induction  in  iron  was  forced  to 
much  higher  values  by  using  a  larger  electro-magnet  and  by 
turning  down  the  neck  of  the  bobbin.  The  extent  to  which 
concentration  of  induction  in  the  neck  may  be  carried  depends 
on  the  proportion  which  the  sectional  area  of  the  neck  bears  to 
that  of  the  pole  from  which  the  lines  converge.  In  the  follow- 


*  Ewing  and  Low,  PM.  Trans.,  CLXXX.,  1889,  A,  p.  221  ;  Rep.  Brit, 
£gsoc.,  1887,  p.  586. 


144  MAGNETISM   IN   IRON. 

Ing  experiment  the  section  of  the  neck  was  reduced  until  it 
was  finally  only  yj^  that  of  either  pole.  The  magnet — an 
exceptionally  powerful  one,  belonging  to  the  Physical  Laboratory 
of  Edinburgh  University — was  excited  with  64,000  ampere- 
turns,  and  its  force  was  concentrated  from  poles  about  10  cms. 


Fia.  67.— Pole-pieces  and  Bobbin  used  in  the  Isthmus  Method. 


square  upon  a  neck  or  isthmus  2'66  mm.  in  diameter  and 
3-5  mm.  long.  Fig.  67  is  a  full-size  sketch  of  the  poles  with  the 
bobbin  in  its  place  after  its  neck  had  been  reduced  to  the 
smallest  diameter.  The  dimensions  are  entered  in  millimetres. 
The  bobbin  c  was  the  same  bobbin  of  annealed  Lowmoor 
wrought  iron  as  had  been  used  in  the  earlier  experi- 


THE   ISTHMUS   METHOD.  145 

ments,  a  pair  of  separate  conical  pieces  bb  being  interposed 
to  connect  its  ends  with  the  pole-faces  a  a.  With  each  reduction 
in  the  size  of  the  neck  a  higher  value  of  B  was  reached; 
finally,  when  its  diameter  was  0-266  mm.,  the  induction  B  was 
45,350,  and  the  force  in  the  space  immediately  surrounding  the 
neck  was  24,500.  From  other  experiments  we  may  infer  that 
this  was,  as  nearly  as  possible,  equal  to  the  actual  magnetic 
force  within  the  metal :  hence  the  result  may  be  written  thus : — 

H  B  I  p 

24,500         45,350         1,660         1-85 

No  attempt  was  made  to  reduce  the  neck  further,  and  this 
is  the  highest  induction  that  has  hitherto  been  recorded  in  any 
experiment.  There  is  no  reason  to  doubt,  however,  that 
higher  values  of  H  and  of  B  might  be  obtained  by  using  an 
electro-magnet  of  greater  size  and  power. 

§  95.  Theory  of  the  Isthmus  Method :  Form  of  Cone  to 
give  Maximum  Concentration.* — Consider  an  imaginary  section 
through  the  middle  of  the  neck,  at  right  angles  to  the  axis  of 
the  bobbin.  It  is  clear  that  there  is  no  discontinuity  between 
the  magnetic  force,  at  points  in  this  plane,  inside  and  outside 
the  metal,  for  there  is  no  free  magnetism  on  the  surface  of  the 
neck  at  the  middle  of  its  length.  We  have  to  consider  the  con- 
ditions which  will  make  the  magnetic  force  as  nearly  uniform  as 
possible  over  this  medial  section  in  order  that  the  force  just 
outside  the  neck,  which  we  are  able  to  measure,  may  be  fairly 
representative  of  the  force  within  the  substance  of  the  neck 
itself. 

The  magnetic  force  in  the  space  between  the  pole-pieces  is 
made  up  of  two  parts  :  (1)  the  electro-magnetic  force  directly 
produced  there  by  the  current  in  the  magnet  coils;  and  (2)  the 
force  due  to  free  magnetism,  distributed  for  the  most  part  over 
the  pole-faces.  The  first  of  these  forms  a  comparatively  small 
part  of  the  whole;  and  its  value  is  sensibly  uniform  at  such  small 
distances  from  the  axis  as  those  with  which  we  are  now  con- 
cerned. In  considering  the  conditions  which  will  secure  the 
greatest  strength  or  the  greatest  uniformity  in  the  field  at  the 

*  Parts  of  this  and  the  succeeding  paragraphs  are  taken  from  the  Paper 
cited  (Phil.  Trans.,  1889,  A,  p.  221). 

L 


146 


MAGNETISM   IN   IRON. 


neck,  we  need  only  deal  with  that  part  of  the  force  which  is 
produced  by  free  magnetism. 

The  free  magnetism  of  the  pole-faces  may  be  treated  as  made 
up  of  a  series  of  co-axial  circular  rings  in  planes  normal  to  the 
axis  of  the  bobbin.  Calling  M  the  whole  free  magnetism  of 
one  of  these  rings  (Fig.  68)  and  r  its  radius,  the  magnetic  force 
F  due  to  it  at  a  point  in  the  axis  at  a  distance  x  from  the  plane 

~\i[x 
of  the  ring  is  —  —   where  I  = 


+  ^      This  force  will  be  a 


d  F 


maximum  when  -  =  0,  that  is,  when 
ax 


which  occurs  when  x  =  —  ~  ;  tan  0=  J^  >  #  =  5  4°  44'      Hence 

V2 
a  series  of  co-axial  rings  will  be  most  advantageously  disposed 


for  producing  force  at  a  point  on  the  axis  if  they  lie  on  a  cone 
having  its  vertex  at  the  point  in  question,  with  a  semi-vertical 
angle  of  54°  44'. 

The  greatest  force  will  be  produced  when  the  pole-pieces  are 
themselves  saturated,  so  that  I  reaches  its  limiting  value  in  all 
parts  of  the  metal.  In  that  case  the  distribution  of  density 
from  ring  to  ring  is  uniform.  The  surface  density  of  free 
magnetism  at  any  point  of  a  sloping  pole-face  is  lsin#,  where 
0  is  the  slope  of  the  face  to  the  axis  of  magnetisation.  The 


THE    ISTHMUS    METHOD.  147 

whole  quantity  in  each  ring  is  I  multiplied  by  the  area  of  the 
ring  projected  upon  a  plane  normal  to  the  axis — a  quantity 
which  is  independent  of  the  slope  of  the  cone.  We  have, 
therefore,  the  same  series  of  attracting  rings  to  deal  with 
whatever  be  the  slope  of  the  convergent  faces,  and  whether 
that  slope  be  uniform  or  not.  Given,  then,  a  certain  diameter 
for  the  neck  of  the  bobbin  to  be  magnetised,  the  greatest 
magnetic  force  will  be  produced  at  the  middle  of  the  axis  of 
the  neck  when  the  pole-pieces  are  saturated  and  when  we 
make  the  expanding  ends  and  pole-faces  in  the  form  of  cones, 
with  a  semi-angle  of  54°  44',  and  with  their  vertices  at  the 
middle  of  the  neck. 

This  determines  what  may  be  called  the  cones  of  maximum 
concentrative  power.  In  practice  cones  intended  to  produce 
as  great  a  concentration  as  possible  should  have  a  somewhat 
greater  semi-angle — say  60°  or  so — because  of  the  defective 
saturation  of  the  pole-pieces. 

§96.  Greatest  Magnetising  Force  producible  by  Means  of 
Cones. — With  a  cone  of  any  semi-angle  6,  magnetised  to  a 
uniform  intensity  I0,  the  surface  density  of  free  magnetism  is 
|0  sin  0,  and  the  force  at  the  vertex  due  to  a  ring  at  an  axial 
distance  x,  of  radius  r,  and  of  length  dl,  measured  along  the 
slope,  is 

27rrdl.\QsmO.^,  or  2  TT  I0  sin2  $  cos  0-. 

The  whole  force  at  the  vertex  is 
2  TT  sin2  6  cos  0 


a  being  the  radius  of  the  neck  on  which  the  cone  converges, 
and  b  the  radius  of  the  base  to  which  it  spreads. 

Hence  (treating  I0  as  uniform),  with  a  pair  of  truncated 
cones,  joined  by  a  neck  at  the  middle  of  which  they  have  their 
common  vertex,  the  whole  force  there  is 

F  =  47rl0sin20cos<91og  A, 
ea 

which,  for  convenience  of  calculation,  may  be  written 

F  =  28-935  I0  sin2  0  cos  6  Iog10  —. 

a 


148  MAGNETISM   IN   IRON. 

Applying  this  to  the  cones  of  maximum  concentrative  power 

(§95),  in  which  sin  6=  ^/f  and  cos  0  =  -L-  . 

V3 

Fma,  =  11-137  I0log10-, 
a 

and  the  greatest  value  of  the  force  will  be  obtained  when  1° 
has  the  saturation  value  (of  say  1,700  C.-G.-S.  units  for  soft 
wrought  iron),  in  which  case 

F      =  18930  lo 


ma, 


an  expression  which  measures  the  greatest  possible  force  which 
the  isthmus  method  of  magnetisation  can  apply  at  a  point  in 
the  axis  of  the  bobbin  (over  and  above  the  small  force  which  is 
directly  produced  by  the  magnet  coils).  It  is  not  practicable 
to  produce  quite  so  large  a  force,  because  the  magnet  poles 
cannot  be  fully  saturated. 

§  97.  Form  of  Cone  to  give  Most  Uniform  Field.  —  The 
cone  of  maximum  concentrative  power  is  not  the  form  best 
suited  for  producing  a  uniform  magnetic  force  throughout  the 
neck.  It  makes  the  field  rather  stronger  at  places  near  the 
axis  than  on  the  axis  itself.  To  make  the  field  as  nearly  uniform 
as  possible  in  and  close  to  the  neck  we  must  slope  the  cone  at 

.72  "p 

such  an  angle  that  -  =0,  a  condition  which  secures  that 
dx* 

72  Tji  J2  "p1 

-  and  -  shall  also  be  zero.  This  condition  is  satisfied 
dy*  dz* 

9x     15  a*     A 

when  T'-^-=0' 

which  makes  x  =  r  j$}  tan  0=^/1  5  0=39°  14'. 

In  other  words,  the  best  approximation  to  a  uniform  field 
(the  pole-pieces  being  saturated)  is  reached  when  the  pole-faces 
are  cones  converging  upon  the  middle  of  the  neck,  with  a  semi- 
vertical  angle  of  39°  14'.  When  the  cones  have  this  form,  and 
the  neck  is  very  narrow  in  comparison  with  the  base,  the  field 
is  so  nearly  uniform  that  the  magnetic  force  in  a  narrow  ring 
of  space  round  the  neck  and  close  to  it  may  be  taken  to  repre- 


THE    ISTHMUS   METHOD. 


149 


sent,  without  sensible  error,  the  force  within  the  neck  itself,  and 
there  is  no  practical  variation  of  the  force  in  the  neck  from  end 
to  end,  or  from  side  to  centre. 

With  cones  of  this  form  the  concentration  of  force  upon  the 
neck  is  less  than  in  the  former  case.  Using  the  same  notation 
as  before  the  force  is 

15,240  Iog10  *, 
a 

in  the  event  of  the  poles  being  of  wrought  iron  and  fully 
saturated. 


,  Fia.  69. 


FIG.  70 


The  difference  between  the  two  cases  is  illustrated  by  Figs. 
69  and  70,  where  curves  are  drawn  to  show  the  force  exerted  at 
various  points  on  the  axis  by  a  single  pair  of  rings,  forming 
parts  of  conical  pole-faces  which  have  a  common  vertex.  In 
Fig.  69  the  rings  are  parts  of  cones  of  maximum  concentrative 
power;  in  Fig.  70  they  are  parts  of  cones  shaped  to  produce  the 
best  possible  approximation  to  a  uniform  field.  The  rings  are 
taken  equal  in  both  cases,  so  that  the  height  to  which  the  curves 
rise  in  the  middle  will  serve  for  comparison  of  the  forces :  the  flat- 


150 


MAGNETISM    IN    IRON. 


ness  of  the  curve  in  Fig.  70  shows  the  superiority  of  that  form 
of  cone  in  respect  to  uniformity  of  field.  With  actual  conical 
pole-pieces,  the  force  produced  in  the  neck  is,  of  course,  made  up 
of  the  sum  of  the  forces  due  to  pairs  of  rings  like  these  dis- 
tributed over  the  whole  conical  surface. 

§  98.  Further  Experiments  with  Wrought  Iron. — In  the 
following  experiments  bobbins  were  used  of  a  shape  suited  to 
give  a  fair  approximation  to  a  uniform  field,  and  hence  the 
outside  field  close  to  the  neck  is  taken  as  the  measure  of  H  : — 

TABLE  XL — Lowmoor  Wrought  Iron. 


H 

B 

1 

A* 

3,080 

24,130 

1,680 

7'83 

6,450 

28,300 

1,740 

4-39 

10,450 

32,250 

1,730 

3-09 

13,600 

35,200 

1,720 

2-59 

16,390 

36,810 

1,630 

2-25 

18,760 

39,900 

1,680 

2-13 

18,980 

40,730 

1,730 

215 

TABLE  XII. — Sivedish  Iron,  "  LsLancash."  Brand. 


H 

B 

1 

A* 

1,490 

22,650 

1,680 

15-20 

3,600 

24,650 

1,680 

6-85 

6,070 

27,130 

1,680 

4-47 

8,600 

30,270 

1,720 

3-52 

18,310 

38,960 

1,640 

2-13 

19,450 

40,820 

1,700 

210 

19,880 

41,140 

1,700 

2-07 

TABLE  *XIII.—Fine  Swedish  Iron,  (  L  J  Brand. 


H 

B 

. 

A* 

5,310 

25,670 

1,620 

4-83 

17,680 

38,080 

1,620 

215 

19,240 

39,540 

1,620 

2-06 

OAST    IRON   AND    STEEL    IN    VERY    STRONG    FIELDS.  151 

In  this  last  iron,  which  is  described  as  the  finest  and  most  ex- 
pensive iron  used  in  commerce,  made  by  the  Walloon  process,  the 
saturation  value  of  I  seems  to  be  specifically  rather  less  than  in 
other  brands.  The  saturation  value  usually  found  in  wrought 
iron  may  be  stated  to  be,  in  round  numbers,  1,700.  The  state 
of  saturation  is  practically  reached,  in  soft  metal,  with  a  force 
of,  say,  2,000  C.-G.-S.  units;  from  this  force  upwards  no 
material  change  can  be  observed  in  I,  though  the  force  be 
increased  ten-fold. 

§  99.  Cast  Iron  and  Steel  in  very  Strong  Fields. — In 
cast  iron  the  highest  value  to  which  B  was  pushed  in  these 


Fio.  71.— Experiments  on  Vickers'  Tool  Steel. 

experiments  was  31,760,  with  the  result  of  reducing  the  per- 
meability to  1*9.  The  saturation  value  of  I  in  the  sample 
tested  was  1,240,  and  saturation  was  practically  complete 
under  a  force  of  4,000. 

In  hard  steel  the  state  of  complete  saturation  is  not  so  easily 
reached.  The  following  test,  which  was  made  with  a  sample  of 
Yickers' tool  steel  possessing  much  coercive  force,  exemplifies  this. 
The  test  piece  formed  the  central  part  of  a  bobbin  with  wrought- 
iron  cones,  built  up  in  the  manner  shown  in  Fig.  71.  By  re- 
moving one  of  the  cones,  a  loose  coil  on  the  neck  could  be 


152 


MAGNETISM   IN   IRON. 


slipped  off  to  determine  the  residual  magnetism,  which  in  this 
case  formed  a  considerable  part  of  the  whole.  (The  residual 
induction  in  the  neck  was  about  8,000.)  It  may  be  doubted 
whether  saturation  was  complete  even  in  the  strongest  field. 


TABLE  XIV.—  Victors'  Tool  Steel. 


H 

B 

1 

V- 

6,210 

25,480 

1,530 

4-10 

9,970 

29,650 

1,570 

2-97 

12,120 

31,620 

1,550 

2-60 

14,660 

34,550 

1,580 

2-36 

15,530 

35,820 

1,610 

2-31 

There  appear,  however,  to  be  specific  differences  in  the  satu- 
ration values  of  I  in  different  steels.  In  the  following  Table  a 
summary  of  the  results  of  experiments  with  other  steels  is  given, 
showing  in  each  case  the  highest  force  applied  and  the  highest 
induction  reached,  along  with  (approximate)  corresponding  values 
of  I  and  /*. 

TABLE  XV. — Steel  of  Various  Qualities. 


Outside  field 

B-  outside  field 

B 

Description  of  Steel. 

(=H  nearly). 

B 

47T 

(=|  nearly). 

Outside  field 
(=A*  nearly). 

1.  Bessemer  steel,  contain- 
ing about  0'4  per  cent, 
of  carbon 

17610 

39,880 

1,770 

2'27 

2.  Siemens-Martin       steel, 
containing  about  0'5  per 
cent,  of  carbon    

18,000 

38,860 

1,660 

2'16 

3.  Crucible  steel  for  making 
chisels,  containing  about 
0'6  per  cent,  of  carbon  .  .  . 
4.  Finer  quality  of  crucible 
steel    for   chisels,    con- 
taining   about  0'8   per 
cent  of  carbon  .. 

19,470 
18330 

38,010 
38,190 

1,480 
1,580 

1-95 

2-08 

5.  Crucible  steel,  containing 
1  cer  cent,  of  carbon    .  .  . 
6.  Whitworth    fluid  -  com- 
pressed  steel    

19,620 
18,700 

37,690 
38,710 

1,440 
1,590 

1-92 
2-07 

NICKEL  AND   COBALT   IN   STRONG   FIELDS. 


153 


§100.  Hadfield's  Manganese  Steel  in  Strong  Fields. — Kefer- 
ence  has  been  made  in  §70  to  the  remarkable  absence  of 
magnetic  susceptibility  shown  by  this  steel,  which  contains 
about  12  per  cent,  of  manganese  and  1  per  cent,  or  less  of 
carbon.  In  fields  of  ordinary  strength  this  alloy  has  a  sensibly 
constant  permeability  of  about  1  '3,  as  Hopkinson's  experiments 
have  shown.*  Application  of  very  strong  fields,  by  means  of 
the  isthmus  method,  shows  that  the  permeability,  even  under 
very  great  forces,  remains  constant  as  nearly  as  may  be  judged. 
One  might  expect  that  a  material  which  resists  magnetisation 
so  strongly  would  show  much  coercive  force  ;  the  reverse,  how- 
ever, is  the  case.  Even  the  strongest  force  is  unable  to  pro- 
duce more  than  a  trace  of  residual  magnetism.  The  following 
is  one  of  several  experiments  which  agree  in  showing  that  the 
permeability  of  manganese  steel,  under  any  force  up  to  10,000 
C.-G.-S.  units,  is  practically  constant  with  a  value  of  about  1*4. 
This  permeability  is  so  low  that  when  the  field  is  weak,  the  metal 
takes  up  scarcely  any  magnetism ;  on  the  other  hand,  since 
the  permeability  retains  the  same  value  in  very  strong  fields, 
a  respectably  high  intensity  of  magnetisation  may  be  produced 
by  applying  a  sufficiently  strong  force.  The  variations  of  p  in 
Table  XVI.  are  irregular,  and  are  no  greater  than  may  be 
ascribed  to  errors  of  observation. 

TABLE  XVI. — Hadfield's  Manganese  Steel. 


H 

B 

1 

/* 

1,930 

2,620 

55 

1-36 

2,380 

3,430 

84 

1-44 

3,350 

4,400 

84 

1-31 

6,920 

7,310 

111 

1-24 

6,620 

8,970 

187 

1-35 

7,890 

10,290 

191 

1-30 

8,390 

11,690 

263 

1-39 

9,810 

14,790 

396 

1-51 

§  101.  Nickel  and  Cobalt  in  Strong  Fields.— With  nickel 
and  cobalt  a  state  of  complete  saturation  is  reached  without 


*  Phil.  Trans.,  1885,  p.  462. 


154 


MAGNETISM    IN   IRON. 


difficulty,  as  the  following  observations  show.  In  the  two 
specimens  of  nickel  tested  (Tables  XVII.  and  XVIII.)  the 
saturation  values  of  I  were  about  400  and  515  respectively ; 
the  difference  is  perhaps  due  to  differences  in  the  amount  of 
iron  present :  neither  specimen  was  pure.  The  saturation 
value  of  I  in  cobalt  (Table  XIX.)  appears  to  be  1,300,  which  is 
a  little  greater  than  the  value  in  cast  iron. 

TABLE  XVII. — Hard-drawn  Nickel  (with  0'56  per  cent. 
of  Iron). 


H 

B 

1 

/* 

2,220 

7,100 

390 

3-20 

4,440 

9,210 

380 

2-09 

7,940 

12,970 

400 

1-63 

14,660 

19,640 

400 

1-34 

16,000 

21,070 

400 

1-32 

TABLE  XVIII. — Annealed  Nickel  (with  0'75  per  cent, 
of  Iron). 


H 

B 

1 

A* 

3,450 

9,850 

510 

2-86 

6,420 

12,860 

510 

2-00 

8,630 

15,260 

530 

1-77 

11,220 

17,200 

480 

1-53 

12,780 

19,310 

520 

1-51 

13,020 

19,800 

540 

1-52 

TABLE  XIX. — Cobalt  (with  1-66  per  cent,  of  Iron). 


H 

B 

1 

/* 

1,350 

16,000 

1,260 

12-73 

4,040 

18,870 

1,280 

4-98 

8,930 

23,890 

1,290 

2-82 

14,990 

30,210 

1,310 

2-10 

CONCLUSIONS   FROM   ISTHMUS    EXPERIMENTS. 


155 


§  102.  Summary  of  Conclusions  from  Isthmus  Experi- 
ments.— To  sum  up  the  results  which  have  been  arrived  at  by 
means  of  the  isthmus  method,  the  concluding  paragraph  of  the 
Paper  from  which  these  figures  are  taken  may  be  quoted.* 

Under  sufficiently  strong  magnetising  forces  the  intensity  of 
magnetisation,  I,  reaches  a  constant  or  very  nearly  constant 
value  in  wrought  iron,  cast  iron,  most  steels,  nickel,  and  cobalt. 
The  magnetic  force  at  which  I  may  be  said  to  become  practi- 
cally constant  is  less  than  2,000  C.-G.-S.  units  for  wrought  iron 


of    o"  IN"    ^    <o    of    o"   e-f    •** 

lHiHt-lFHiHC4BI<N 

Induction  B. 
FIG.  72.— Permeability  of  Magnetic  Metals  when  very  Strongly  Magnetised. 

and  nickel,  and  less  than  4,000  for  cast  iron  and  cobalt.  In 
stronger  fields  the  relation  of  magnetic  induction  to  magnetic 
force  may  be  expressed  by  the  formula 

B  =  H  +  constant. 

For  the  particular  specimens  tested,  the  value  of  this  con- 
stant (4  TT  I)  is  about  21,360  in  wrought  iron,  15,580  in  cast 
iron,  5,030  and  6,470  in  nickel,  and  16,300  in  cobalt. 

The  experiments  give  a  definite  meaning  to  the  term  "  satu- 
ration," as  applied  to  magnetic  state.  When  magnetism  is 

*  Ewing  and  Low,  Phil.  Trans.,  1889  A,  p.  242. 


156  MAGNETISM   IN   IRON. 

measured  by  the  induction  B,  the  term  saturation  is  inapplic- 
able ;  there  is  apparently  no  limit  to  the  value  to  which  the 
induction  may  be  raised.  But,  when  we  measure  magnetisa- 
tion by  the  intensity  of  magnetism  I,  we  are  confronted  with  a 
definite  limit — a  true  saturation  value,  which  is  reached  or 
closely  approached  by  the  application  of  a  comparatively  mode- 
rate magnetic  force.  There  is  nothing  to  show  that  the  ap- 
proach to  this  limit  is  not  asymptotic ;  but  in  wrought  iron  it 
is  practically  reached  before  the  magnetic  force  rises  to  2,000 
C.-G.-S.,  and  after  that  a  ten-fold  increase  in  the  force  produces 
no  material  change  in  the  intensity  of  magnetism. 

The  results  are  further  summarised  in  Fig.  72,  which  give? 
curves  showing  the  relation  of  the  permeability  ft,  to  the  induc- 
tion B  drawn  from  the  data  supplied  by  experiments  on — 

(1.)  Swedish  wrought-iron  (Table  XII.). 

(2.)  Vickers'  tool  steel  (Table  XIV.). 

(3.)  Cobalt  (Table  XIX.). 

(4.)  Cast  iron  (Table  X.,  and  other  data). 

(5  and  6.)  Nickel  (Tables  XVIII.  and  XVII.) 

(7.)  Hadfield's  manganese  steel  (Table  XVI.). 

§  103.  Apparatus  for  Applying  the  Isthmus  Method. — In 
applying  the  isthmus  method  it  is  desirable  to  be  able  to  turn 
the  bobbin  round  suddenly  between  the  magnet  poles,  in  order 
to  determine  the  ballistic  effect  produced  by  reversal  of  its  mag- 
netism. An  arrangement  used  by  the  writer  for  this  purpose  is 
shown  in  Figs.  73  and  74.  Fig.  73  shows  the  electro-magnet  as  a 
whole,  and  Fig.  74  is  a  sectional  sketch  of  the  pole-pieces  and 
bobbin  and  bobbin-holder.  The  poles,  which  are  four  inches  in 
diameter,  admit  of  having  the  distance  between  them  adjusted, 
and  a  brass  piece  a  a  is  fitted  between  them,  having  hollow  cones 
turned  out  of  its  ends,  into  which  the  conical  pole-pieces  fit 
exactly.  This  holds  the  pole-pieces  at  the  proper  distance  apart. 
Through  the  brass  piece,  a  a,  a  cylindrical  hole  is  bored,  extending 
through  from  side  to  side,  and  removing  the  points  of  the  conical 
pole-pieces.  Into  this  hole  the  bobbin-holder,  c  c,  with  the  bobbin, 
d,  is  slipped  from  one  side.  The  part  which  projects  outside  of 
a  has  a  shoulder  turned  on  it,  which,  when  it  is  pressed  home, 
brings  the  axis  of  the  bobbin  just  into  line  with  the  axis  of  the 


APPARATUS   FOR  APPLYING  THE    ISTHMUS   METHOD.          157 


FIG.  73.— Electro-Magnet  for  the  Isthmus  Method. 


FIG.  74. — Section  through  Bobbin  and  Bobbin-holder. 


158  MAGNETISM   IN    IRON. 

pole-pieces.  The  bobbin-holder  is  of  brass,  and  is  made  of  two 
pieces,  c  c,  between  which  the  bobbin  d  is  clutched,  the 
pieces  being  fastened  together  by  long  screws  put  in  from  the 
end  of  the  holder,  which  pass  clear  of  the  bobbin  on  each 
side  of  the  neck.  There  is  a  little  clearance  round  the  neck 
to  give  room  for  the  induction  coils  to  be  wound,  and  the 
leading  wires  from  these  pass  out  through  a  hole  in  the 
end  of  the  holder.  The  bobbin  d  has  its  ends  turned  so 
that  they  virtually  form  part  of  the  cylindrical  surface  of  the 
holder,  and  it  fits  exactly  into  the  cylindrical  hole  between  the 
pole-piece  ends.  The  handle  b  attached  to  the  holder  allows 
the  bobbin  to  be  suddenly  reversed,  and  a  stop  is  provided  at  « 
to  make  the  movement  exactly  180°.  The  electro-magnet  of 
Fig.  73  is  furnished  with  two  pairs  of  conical  pole-pieces,  one 
pair  sloped  to  give  maximum  concentrative  power  (§  95)  and  the 
other  pair  to  give  maximum  uniformity  in  the  field  (§  97).  For 
each  pair  a  bobbin  of  the  iron,  or  other  metal  to  be  tested,  is 
turned  with  the  same  slope,  and  for  each  pair  there  is  a  dis- 
tance-piece and  bobbin-holder  to  correspond. 

§  104.  Experiments  by  du  Bois  with  Strong  Fields.  Optical 
Method. — The  conclusions  which  were  arrived  at  by  means  of 
the  isthmus  method,  as  to  the  existence  of  a  finite  limit  to  the 
intensity  of  magnetism,  and  as  to  the  manner  in  which  that 
limit  is  approached  when  strong  magnetic  forces  are  applied,  have 
received  independent  confirmation  from  the  later  experiments 
by  H.  E.  J.  G.  du  Bois,*  in  which  a  novel  and  highly  interest- 
ing method  of  measurement  was  introduced  and  used  with 
excellent  effect.  The  method  is  an  optical  one,  based  on  Dr. 
Kerr's  discovery,!  that  when  plane  polarised  light  is  reflected  by 
a  magnet  pole  the  plane  of  polarisation  is  turned,  through  an 
angle  which  depends  on  the  intensity  of  the  magnetisation. 
Before  this  fact  could  be  turned  to  account  for  the  purpose  of 
measuring  magnetism,  it  was  necessary  to  know  exactly  what 
relation  holds  between  the  magnetism  of  the  reflecting  metal 
and  the  angle  of  rotation  of  the  polarised  ray.  This  question 


*  Du  Bois,  Phil.  Mag.,  April,  1890,  p.  293. 

tKerr,  Brit.  Ass.  Report,  1876,  p.  40  ;  Phil.  Mag.,  May,  1877,  p.  321. 


EXPERIMENTS   BY   DU   BOIS    WITH    STRONG   FIELDS.  159 

was  made  the  subject  of  a  preliminary  investigation  by 
du  Bois,*  who  answered  it  by  examining  the  rotation  of  the  ray 
when  reflected  from  small  surfaces,  ground  flat,  and  polished, 
on  ellipsoids  of  iron,  steel,  nickel,  and  cobalt,  the  ellipsoids  being 
magnetised  by  means  of  a  surrounding  coil.  He  found  that 
the  relation  is  of  a  very  simple  kind :  the  rotation  of  the 
polarised  ray  is  proportional  to  the  intensity  of  magnetism  I, 
and  may,  therefore,  be  written  equal  to  K  I  when  K  is  a 
constant!  coefficient,  to  which  du  Bois  gave  the  name  of 
Kerr's  constant.  He  determined  numerical  values  of  K  for 
iron,  steel,  nickel,  and  cobalt.  Knowing  these,  it  is,  of  course, 
possible  to  invert  the  process,  and  use  the  measurements  of 
optical  rotation  to  determine  values  of  I  in  cases  where  they 
are  not  otherwise  known. 

This  du  Bois  has  done  in  a  way  that  will  be  readily  under- 
stood by  reference  to  Fig.  75  (taken  from  his  second  Paper). 
P!  P2  are  the  poles  of  a  powerful  electro-magnet,  made  conical, 
as  in  the  isthmus  method,  for  the  purpose  of  concentrating 
magnetic  force  in  the  neighbourhood  of  the  apex.  Through 
one  of  them  (P2)  a  hole  is  bored  to  allow  the  polarised  light  to 
come  to,  and,  after  reflexion,  to  return  from,  the  polished  plate 
M,  which  is  a  small  piece  of  the  metal  whose  magnetism  is  to  be 
examined,  and  is  in  contact  with  the  magnet  pole  Pr  When 
the  electro-magnet  is  excited,  M  is  very  strongly  magnetised, 
and  the  value  of  I  in  it  is  measured  by  observing  the  angle  of 
rotation  of  the  polarised  ray  and  dividing  that  by  the  known 
value  of  Kerr's  constant,  previously  determined  by  experi- 
ments with  a  magnetised  ellipsoid  of  the  same  material.  J  J 
is  a  steam  jacket  which  was  used  to  maintain  the  plate 
at  a  temperature  approaching  100°  C  in  some  of  the  experi- 
ments. 

We  have  said  nothing  yet  about  the  manner  of  finding  the 
magnetic  force  H  acting  on  the  plate  M.  It  was  not  found 
directly  ;  what  was  directly  found  was  the  induction  B.  When 
I  and  B  are  known,  H  may  of  course  be  deduced  by  means  of 
the  equation  H  =  B  -  4  TT  I.  Now,  in  determining  B  in  the  plate, 

*  Phil.  Mag.,  March,  1890,  p.  263. 

t  Constant,  that  is  to  say,  for  any  one  metal,  and  for  any  one  wave- 
length of  light.  K  differs  much  for  light  of  different  wave-lengths. 


160 


MAGNETISM    IN   IRON. 


it  is  to  be  borne  in  mind  that  there  is  no  discontinuity  in  lines 
of  induction.  The  lines  of  induction  pass  out  of  the  plate 
normal  to  its  surface,  and  B  within  the  plate  has  the  same  value 
as  the  induction  (or  what  is  there  the  same  thing,  the  magnetic 
force)  in  the  air  immediately  in  front  of  the  plate.  This  fact 
was  taken  advantage  of  in  determining  B.  It  might  have  been 
measured  ballistically  by  slipping  out  an  induction  coil  laid  on 
the  face  of  M,  or  wound  round  the  circumference  of  M ;  but 


FIG.  75. — Optical  Method  of  Measuring  Magnetism  in  Strong 
Fields  (du  Bois). 

the  plan  actually  used  by  du  Bois  was  an  optical  one.  A  thin 
glass  plate  G,  with  a  silvered  back  S,  could  be  interposed  in 
the  path  of  the  ray,  immediately  in  front  of  the  plate  M — that 
is  to  say,  at  the  place  where  a  determination  of  the  magnetic 
field  was  wanted.  A  plane  polarised  ray  passing  through 
a  plate  of  glass  in  a  magnetic  field  suffers  rotation,  as 
Faraday  originally  showed,  and  the  amount  of  this  rotation  is 
proportional  to  the  magnetic  force  and  to  the  thickness  of  the 
plate.  In  the  present  case  the  ray  passed  twice  through  the 


RESULTS    OF    OPTICAL    MEASUREMENTS.  161 

glass  plate.  The  plate  was  standardised  by  comparing  the  mag- 
neto-optic rotation  in  it  with  that  in  bisulphide  of  carbon,  the 
value  of  which  is  well  known. 

Thus,  by  means  of  two  independent  optical  measurements, 
there  were  determined,  first,  the  value  of  I  in  the  strongly 
magnetised  plate  M  of  iron  or  other  magnetic  metal  (by  observ- 
ing the  rotation  of  a  polarised  ray  reflected  by  M),  and,  second, 
the  value  of  B  in  the  same  plate,  this  last  being  equal  to  the 
magnetic  force  acting  on  the  glass  plate  when  the  glass  plate  was 
put  in  front  of  the  other,  and  being  measured  by  observing  the 
rotation  of  a  polarised  ray  reflected  from  the  silvered  back  of 
the  glass. 

§  105.  Results  of  Optical  Measurements. — The  general 
results  which  the  optical  method  has  yielded  in  the  hands  of 
du  Bois,  as  to  the  action  of  strong  fields,  are  in  complete  agree- 
ment with  those  obtained  by  means  of  the  isthmus  method  and 
narrated  above.  The  magnetic  force  was  not  pushed  to  such 
high  values,  but  the  values  were  high  enough  to  show 
that  a  close  approach  to  a  limiting  maximum  of  I  had  been 
reached.  With  nickel,  the  force  H  was  raised  to  nearly  13,000, 
with  cobalt  to  8,500,  with  steel  to  4,500,  .and  with  soft  iron  to 
2,500.  The  limiting  values  towards  which  I  tended  appeared  to 
be  530  in  nickel,  1,200  in  cobalt,  and  1,630  in  steel  (a  hard 
English  cast  steel).  In  the  case  of  iron,  the  experiments  were 
rather  less  satisfactory,  but  pointed  to  a  limit  between  1,700 
and  1,750.  These  values  are  given  for  observations  made  when 
the  specimens  were  at  a  temperature  of  100°C. ;  at  ordinary 
temperatures  the  values  would  be  rather  greater,  as  was  shown 
by  comparative  tests  at  100°  C.  and  at  0°  C.  It  is  clear  that 
these  numbers  are  in  good  general  agreement  with  those  that 
have  been  stated  already,  §§  98-102. 

The  following  data  are  taken  from  du  Bois'  Paper.  Table 
XX.  relates  to  a  specimen  of  cast  cobalt,  tested  at  100°  C., 
containing  5 '8  per  cent,  of  nickel,  and  0'8  per  cent,  of  iron. 
An  additional  observation,  made  in  the  strongest  field, 
showed  that  I  at  0°  C.  was  1,232.  Table  XXI.  relates  to  a 
specimen  of  hard-drawn  best  nickel  wire,  stated  to  contain  99 
per  cent,  of  nickel.  Here,  again,  a  low-temperature  observation 
in  the  strongest  field  made  the  value  of  I  at  0°  C.  to  be  579. 

M 


162 


MAGNETISM    IN    IRON. 


TABLE  XX..— Cobalt  in  Strong  Fields  at  100° C. 


H 

B 

1 

V- 

860 

14,180 

1,060 

16-49 

2,500 

16,750 

1,134 

6-70 

4,800 

19,550 

1,174 

4-07 

6,870 

21,710 

1,181 

3-16 

8,350 

23,330 

1,192 

279 

TAB*LE  XXI. — Nickel  in  Strong  Fields  at  100° 


H 

B 

1 

/* 

550 

6,420 

453 

11-67 

3,410 

9,920 

518 

3-12 

6,290 

12,850 

522 

2-57 

9,600 

16,250 

527 

1-69 

12,620 

19,220 

525 

1-52 

On  making  optical  observations  with  a  specimen  of  Hadfield's 
manganese  steel — the  non-magnetic  steel  spoken  of  in  §  70 — it 
was  found  that  the  amount  of  magneto-optic  rotation  of  the 
polarised  ray  varied  considerably  when  the  ray  was  reflected 
from  different  parts  of  the  same  polished  surface,  from  which 
result  du  Bois  infers  that  this  material  is  essentially  hetero- 
geneous, having  relatively  strongly  magnetic  layers  interposed 
between  non-magnetic  or  feebly  magnetic  portions  of  the  mass. 
He  supposes  the  structure  to  be  laminar,  but  so  fine-grained 
that  to  ordinary  tests  it  appears  homogeneous. 

§  106.  Magnetisation  of  Magnetite.— Du  Bois  has  applied 
his  optical  method  to  obtain  absolute  measurements  of  the 
magnetisation  in  strong  fields  of  a  crystal  of  magnetite  (the 
magnetic  oxide  of  iron,  Fe3  04),  which  is  the  only  substance 
that  shares  with  iron,  nickel,  and  cobalt  the  distinction  of  being 
strongly  magnetisable.  The  results  show  that  there  is  a 


EXPERIMENTS    WITH    ELLIPSOIDS. 


163 


limiting  maximum  of  I  in  magnetite  with  the  value  of  about 
350,  and  that  saturation  is  practically  complete  with  a  force  H 
of  1,000  or  1,500  units.* 

§  107.  Experiments  with  Ellipsoids. — Reference  has  been 
made  to  the  preliminary  experiments  with  ellipsoids  by  means 
of  which  du  Bois  determined  the  values  of  Kerr's  constant 
in  specimens  of  the  same  metals  as  were  afterwards  tested  in 
stronger  fields  by  the  optical  process.  ,  The  experiments  with 


FIG.  76 


ellipsoids  were  important,  not  only  as  a  means  towards  that 
end ;  they  are  interesting  in  themselves  because  they  deal  with 
a  portion  of  the  range  in  regard  to  which  we  have  no  other 
experimental  data,  namely,  the  portion  which  extends  from 
H  =  200  or  so  to  H  =  1,200  or  1,300.  With  respect  to  higher 
forces,  we  have  the  results  of  the  isthmus  and  of  the  magneto- 
optic  methods;  with  respect  to  lower  forces,  we  have,  of 
course,  a  mass  of  data ;  but  between  the  limits  named  there 
is  a  gap  which  these  experiments  with  ellipsoids  are  the  first 
to  bridge. 

*  Phil.  Mag.,  April,  1890,  p.  301. 


164 


MAGNETISM    IN    IRON. 


The  magnetic  force  was  applied  by  means  of  a  coil,  and  the 
specimen  was  an  ovoid  or  prolate  ellipsoid  of  revolution  18cms. 
long,  and  O'Gcm.  in  diameter,  which  was  kept  at  a  uniform 
temperature  of  0°C.  or  100°C.  by  applying  ice  or  steam.  Its 
magnetisation  was  measured  by  the  ordinary  rnagnetometric 
method,  a  compensating  coil  being  used  to  balance  the  greater 
part  of  the  action  of  the  magnetising  coil  upon  the  magneto- 
meter. The  ratio  of  diameters  being  1 :  30,  a  correction  of  0'052  I 
had  to  be  subtracted  from  the  magnetic  force  due  to  the  coil 
to  find  the  true  magnetic  force  (see  §  26). 

Du  Bois  gives  the  results  in  the  form  of  curves  connecting 
H  with  the  magnetic  moment  per  unit  of  mass — that  is, 
per  gramme.  It  will  be  more  convenient  for  us  to  adhere  to 
the  usual  practice  of  stating  magnetisation  by  the  quantity  I, 
which  is  the  moment  per  unit  of  volume  —that  is,  per  cubic 
centimetre.  The  results  are  accordingly  reduced  to  this  form 
in  the  curves  of  Fig.  76  and  in  Table  XXII.,  the  numbers  in 
which  are  calculated  from  measured  values  of  the  ordinates 
in  du  Bois'  curves.*  The  iron  tested  was  soft  Swedish  wrought 
iron,  carefully  annealed. 


TABLE  XXII. — Iron,  Cobalt,  and  Nickel,  in  Moderately  Strong 

Fields. 


Magnetic  Force, 

Intensity  of  Magnetism,  1. 

H. 

Iron  at  0°C. 

Cobalt  at  100°C. 

Nickel  at  100'C. 

100 

1,410 



313 

200 

1,520 

856 

375 

300 

1,580 

933 

406 

400 

1,627 

988 

428 

500 

1,658 

1,018 

441 

600 

1,677 

1,032 

450 

700 

1,689 

1,048 

456 

800 

1,697 

1,056 

459 

1,000 

1,705 

1,080 

467 

1,200 

1,710 

1,090 

471 

*  Phil.  Mag.,  April,  1890,  Plate  VIII,  Fig.  1. 


EXPERIMENTS    WITH    ELLIPSOIDS.  165 

The  observations  with  cobalt  and  nickel  were  made  at  100°C., 
but  within  the  range  of  magnetic  forces  that  is  dealt  with  here 
the  difference  between  100°C.  and  atmospheric  temperature  has 
but  little  influence  on  the  magnetisation. 

In  Fig.  76  the  same  results  are  given,  and  the  curves  are 
completed  to  the  origin  (in  an  approximate  fashion)  by  sketch- 
ing in,  from  other  data,  the  parts  that  relate  to  lower  forces. 
The  gradient  of  the  cobalt  curve  at  the  upper  end  shows  how 
cobalt  needs  a  stronger  field  than  the  others  to  make  it$ 
magnetisation  approach  closely  to  a  state  of  saturation. 


CHAPTER   VIII. 


EFFECTS   OF   TEMPERATURE. 

§  108.  Effects  of  Temperature  on  Magnetic  Quality  :  Loss 
of  Magnetic  Quality  at  a  High  Temperature. — It  has  been 
known  from  the  time  of  Gilbert  that  when  iron  or  steel  is 
heated  to  bright  redness  it  loses  the  power  of  either  retaining 
magnetism  or  having  magnetism  induced  in  it,  but  recovers  its 
susceptibility  on  cooling.  The  same  thing  happens  at  a  higher 
temperature  with  cobalt  and  at  a  lower  temperature  with  nickel. 
In  general,  the  change  from  the  magnetic  to  the  non-magnetic 
state  occurs  somewhat  suddenly  as  the  temperature  is  raised. 
Thus,  in  one  of  the  experiments  of  Hopkinson — to  be  referred 
to  presently  in  more  detail — a  piece  of  wrought  iron,  subjected 
to  the  action  of  a  weak  magnetic  force,  was  found  to  be  highly 
susceptible  so  long  as  the  temperature  did  not  exceed  775°C. 
In  fact,  up  to  this  point  the  effect  of  heating  was  to  increase 
the  magnetic  susceptibility,  and  at  the  temperature  775°C.  it 
was  many  times  greater  than  when  the  iron  was  cold.  But 
with  further  heating  an  extremely  rapid  loss  of  magnetic  quality 
ensued;  when  the  temperature  had  risen  only  lldeg.  higher, 
to  786°G.,  the  iron  had  become  practically  non-magnetic.  Its 
permeability  was  then  only  1-1,  whereas  at  775°C.  it  had  been 
no  less  than  11,000.  If  the  test  be  made  with  a  strong  mag- 
netic force  instead  of  a  weak  one  the  change  from  the  magnetic 
to  the  non-magnetic  state  is  less  abrupt,  but  it  is  equally  com- 
plete, and  the  same  temperature  as  before  makes  the  iron  non- 
magnetic.* Hopkinson  calls  this  the  critical  temperature.  The 

*  Reference  should  be  made  in  this  connection  to  the  experiments  of 
Baur,  in  the  Paper  "  Experimented  Untersuchungen  iiber  die  Natur  der 
Magnetisiringungsf  unction,"  already  cited.  (Wiedemann'a  Annalen,  1880 
Vol.  XI.) 


CHANGE  OF  PHYSICAL  STATE  AT  CRITICAL  TEMPERATURE.      167 

value  of  the  critical  temperature  varies  in  different  specimens : 
in  samples  of  ordinary  iron  and  steel  it  has  been  found  to  range 
from  690°C.  to  870°C.*  In  an  impure  specimen  of  nickel 
examined  by  Hopkinson  the  critical  temperature  was  310°C.f 

§  109.  Change  of  Physical  State  at  the  Critical  Temperature. 

— The  change  from  the  magnetic  to  the  non-magnetic  state  which 
iron  or  steel  undergoes  at  the  critical  temperature  is  only  one 
of  several  evidences  that  the  metal  then  suffers  a  profound 
change  of  constitution.  One  evidence  of  this  change  is  furnished 
by  the  fact,  observed  in  1869  by  Gore,  that  an  iron  wire,  cooling 
from  a  bright  red  heat,  suffers  a  momentary  elongation  (at  a 
dull  red)  and  then  goes  on  contracting  as  before.  The  change 
shows  itself  in  the  alteration  of  other  physical  qualities  as  well 
as  those  that  have  to  do  with  magnetism.  Thus  Tait  J  has  found 
that  the  thermo-electric  quality  of  iron  alters  in  a  remarkable 
way  at  a  red  heat.  The  alteration  takes  place  suddenly,  and  there 
is  no  reason  to  doubt  that  it  is  associated  with  other  changes 
that  are  brought  about  by  raising  the  temperature  to  the  critical 
value.  Again,  as  the  experiments  of  W.  Kohlrausch§  and 
Hopkinson  ||  have  shown,  the  critical  temperature  is  marked 
by  a  sudden  change  in  the  coefficient  which  expresses  the  effect 
of  temperature  upon  the  electrical  resistance  of  iron.  The 
same  thing  is  true  of  nickel.  Perhaps  the  most  striking  evidence 
that  when  iron  reaches  the  critical  temperature  it  passes — 
more  or  less  suddenly — from  one  condition  to  another  widely 
different  condition,  is  furnished  by  Barrett's  discovery  of 
"  recalescence."  11  Let  a  piece  of  iron  or  steel  be  heated  to 
bright  redness  and  allowed  to  cool  slowly ;  at  a  certain  stage 
(coincident  with  that  at  which  Gore's  phenomenon  occurs), 
the  process  of  cooling  experiences  a  sudden  check.  Heat  ip 
generated  within  the  substance  of  the  metal  as  a  consequence 
of  the  change  which  the  molecular  constitution  suffers  at  this 

*  Hopkinson,  "  Magnetic  and  other  Physical  Properties  of  Iron  at  a 
High  Temperature."  Phil.  Trans.,  1889,  A.,  p.  443. 

t  Hopkinson,  "  Magnetic  Properties  of  an  Impure  Nickel."  Proc.  Roy, 
Soc.,  Vol.  XLIV.,  1888,  p.  317. 

J  Tait,  Trans.  Roy.  Soc.  Edin.,  1873. 

§Kohlrausch,  Wied.^rw.,  Vol.  XXXIII,  1888. 

H  Hopkinson,  loc.  cit. 

IT  Barrett,  Phil.  Mag.,  January,  1874. 


1G8 


MAGNETISM    IN    IRON. 


critical  point;  the  cooling  is  arrested,  and  the  temperature  may 
even  rise,  though  the  loss  by  radiation  is  going  on  as  before.  It 
is  in  hard  steel  that  the  phenomenon  is  most  marked.  So  much 
heat  is  generated  while  hard  steel  passes  from  one  molecular 
state  to  another  at  the  critical  point,  that  there  is  a  very  visible 
reglow;  the  surface  of  the  cooling  metal  turns  for  a  few 
moments  from  a  very  dull  to  a  much  brighter  red,  after  which 
the  colour  continues  to  fade.  The  point  at  which  recalescence 
takes  place  is  the  point  at  which  the  cooling  metal  returns 
from  the  non-magnetisable  to  the  magnetisable  state.  This 
fact,  which  was  surmised  by  Barrett,  has  been  proved  by  the 
experiments  of  Hopkinson,  who  has  measured  the  amount  of 
heat  liberated  during  the  change,  and  has,  moreover,  given 
further  proof  that  recalescence  has  an  intimate  connection 
with  the  recovery  of  magnetic  quality,  by  showing  that  it 
does  not  occur  at  all  in  non-magnetisable  manganese  steel.* 

§  110.  Effects  of  Temperature  below  the  Critical  Point. — 
In  studying  the  effects  of  temperature  we  may  adopt  one  or 
other  of  two  distinct  methods.  We  may  note  the  changes  of 
magnetism  which  are  brought  about  by  varying  the  tem- 
perature, while  the  magnetic  force  is  kept  constant ;  and  as  a 
special  case  of  this  we  may  note  the  changes  of  residual 
magnetism  which  are  brought  about  by  varying  the  tem- 
perature when  there  is  no  magnetic  force  in  action.  Or  we  may 
compare  the  amounts  of  magnetism  which  are  acquired  at  one 
and  another  temperature  when  the  specimen  is  brought  to  the 
temperature  in  question  before  the  magnetic  force  is  applied. 
In  other  words,  we  may  determine  the  form  which  the  curve  of 
I  or  B  and  H  assumes,  when  the  one  or  another  temperature  is 

*  Hopkinson,  loc.  cit.  A  corresponding  perturbation,  involving  absorp- 
tion instead  of  evolution  of  heat,  is  observed  during  the  heating  of  steel 
when  the  magnetic  state  changes  to  non-magnetic.  In  regard  to  the 
general  subject  of  recalescence,  reference  should  be  made  to  the  important 
investigations  of  Osmond  ("  Transformations  du  fer  et  du  carbone,"  M6m. 
de  Vartillerie  de  la  marine,  1888),  which  deal  especially  with  the  tem- 
perature at  which  the  phenomena  of  recalescence  occur.  A  general 
account  of  the  associated  phenomena  will  be  found  in  the  Report  of  a 
Committee  of  the  British  Association  (B.  A.  Report,  1890).  See  also 
papers  by  H.  Tomlinson  and  H.  F.  Newall,  Phil.  Mag.,  1887,  vol.  xxiv., 
pp.  256  and  435. 


EFFECTS  OF  TEMPERATURE  BELOW  THE  CRITICAL  POINT.      169 

maintained  constant  throughout  the  process  of  magnetisation, 
and  may  compare  the  curves  got  in  this  way  at  various  tempera- 
tures. The  two  methods  do  not  yield  identical  results,  because  of 
the  tendency  which  the  magnetic  metals  exhibit  to  oppose  mag- 
netic change — the  property,  namely,  which  gives  rise  to  those 
effects  which  are  included  under  the  general  name  of  magnetic 
hysteresis.  On  account  of  this  property,  which  all  the  mag- 
netic metals  share  more  or  less,  the  magnetic  condition  that  is 
arrived  at  if  we  heat  the  specimen  to  any  assigned  temperature 
first,  and  then  apply  any  assigned  magnetic  force,  is  in  general 
different  from  the  condition  that  is  reached  when  the  order  of 
these  two  operations  is  reversed.  The  same  remark  applies 
with  respect  to  the  changes  of  magnetic  quality  that  are  brought 
about  by  altering  the  state  of  stress,  or  any  other  physical  con- 
dition on  which  the  magnetic  state  of  the  specimen  depends. 
In  the  most  complete  investigations  which  have  yet  been  made 
of  the  effects  of  temperature  on  magnetic  quality,  the  plan  has 
been  followed  of  varying  the  temperature  first,  and  then  study- 
ing the  effects  of  applying  magnetic  force.  In  other  words, 
what  have  generally  been  observed  and  compared  are  the  sus- 
ceptibilities of  the  same  specimen  at  different  temperatures. 

The  experiments  of  Rowland,  Baur,  and  Hopkinson  are  of  this 
kind.  Rowland,*  examining  the  susceptibility  of  nickel  at  two 
temperatures  (5°C.  and  230°C.),  found  that  at  the  higher  tempe- 
rature there  was  much  more  susceptibility  with  respect  to  weak 
magnetic  forces  than  at  the  lower  temperature,  but  less  sus- 
ceptibility with  respect  to  strong  forces.  In  other  words,  when 
the  magnetisation  was  sufficiently  high  the  effects  of  temperature 
upon  susceptibility  became  reversed.  The  maximum  suscepti- 
bility, occurring  as  it  does  when  the  magnetic  force  is  tolerably 
low,  was  greater  at  the  higher  temperature  (some  70  per  cent, 
greater  at  230°C.  than  at  5  deg.).  In  cobalt,  again,  he  showed 
that  the  susceptibility  with  respect  to  low  forces  is  increased  by 
heating — a  specimen  in  which  the  maximum  susceptibility  (K) 
was  11*2  at  5°C.  had  its  maximum  susceptibility  raised  to  18*7 
at  230°C.  The  magnetic  forces  used  by  Rowland  were  not 
strong  enough  to  reverse  this  effect  of  temperature  in  cobalt, 
but  it  is  now  known  that  under  sufficiently  strong  force  the  effect 
is  reversed  in  that  metal,  as  it  is  in  nickel.  Baur  f  has  shown 

*  Kowland,  Phil.  Mag.,  Nov.,  1874.      t  Baur,  Wied.  Ann.,  1880,  Vol.  XL 


170 


MAGNETISM   IN    IRON. 


that  iron  behaves  in  the  same  way.  If  we  compare  the  sus- 
ceptibility of  iron  at  two  temperatures  we  find  that  the  suscep- 
tibility is  greater  at  the  higher  temperature  provided  the 
magnetic  force  does  not  exceed  a  certain  value,  but  less  at  the 
higher  temperature  when  the  force  does  exceed  that  value.  It 
is  with  respect  to  weak  forces  that  the  influence  of  temperature 
is  most  conspicuous.  The  most  complete  experiments  on  the 
subject  are  those  of  Hopkinson,  who  has  given  in  the  two  Papers 
cited  above  (one  dealing  with  iron  and  steel  and  the  other  with 
nickel)  a  series  of  curves  of  magnetisation  for  each  metal  at 
various  temperatures,  ranging  up  to  the  critical  temperature  at 
which  magnetic  quality  disappears.  A  few  of  his  results  may 
be  quoted  as  the  best  means  of  giving  some  account  of  the 
connection  between  magnetic  quality  and  temperature. 

§  111.  Hopkinson's  Experiments  on  the  Magnetisation  of 
Iron  at  Various  Temperatures. — In  these  experiments  the 
specimens  were  rings,  and  the  magnetisation  was  measured 
ballistically  by  reversing  the  magnetising  force.  The  primary 
and  secondary  coils  were  insulated  with  asbestos  paper ;  the 
ring  was  placed  in  a  cast-iron  box,  and  was  heated  by  a  gas 
furnace,  and  its  temperature  was  inferred  from  the  resistance 
of  the  secondary  coil,  which  was  measured  before  and  after  each 
magnetic  experiment. 

A  ring  of  soft  wrought-iron,  for  which  the  critical  tempera- 
ture had  been  found  to  be  about  785°C.,  was  examined  in 
successive  experiments,  at  various  temperatures,  the  curve  of 
B  and  H  being  determined  in  each  case,  while  the  temperature 
was  kept  as  nearly  constant  as  was  practicable.  The  results 
show  that  heating  the  iron  to  a  high  temperature  (short  of  the 
critical  temperature)  augments  its  susceptibility  with  respect 
to  small  magnetic  forces  very  greatly.  On  the  other  hand,  it 
reduces  greatly  the  effect  of  strong  magnetic  forces.  For 
example,  a  force  H  of  0-075  C.-G.-S.  was  found  to  give  the 
following  values  of  B  at  the  temperatures  noted  : — 


Temp. 

B 

10'C. 

37S°C. 

494°C. 

603°C. 

C70°C. 

722°C. 

744°C. 

763eC. 

775°C. 

778*0. 

512 

17 

41 

45 

59 

120 

144 

203 

294 

494 

MAGNETISATION   OP   IRON   AT   VARIOUS   TEMPERATURES. 


171 


At  788°C.,  the  critical  point  having  been  passed,  the  induc- 
tion had  practically  sunk  to  zero.  These  figures  show  well 
the  enormous  increase  of  permeability  which  heating  causes 


0-5  I'D  1-5 

Magnetic  Force  H. 

FIQ.  77. — Magnetisation  of  Iron  at  Various  Temperatures. 

at  early  stages  of  the  magnetising  process.  On  the  other 
hand,  a  force  of  50  units  or  so  gave  less  than  half  as  much 
induction  at  the  upper  as  at  the  lower  end  of  this  range  of 
temperature.  Thus  the  curves  of  B  and  H  taken  at  any  two 


10 


a)  30 

Magnetic  Force  H. 


FIG.  78.— Magnetisation  of  Iron  at  Various  Temperatures. 

temperatures  cross  each  other,  the  one  for  the  lower  tempera- 
ture lying  at  first  below  and  afterwards  above  the  other.  Hop- 
kinson  has  expressed  his  results  in  curves  of  this  kind,  some  of 
which  are  copied  in  Figs.  77  and  78.  Curve  I.  in  these  figures 


172 


MAGNETISM   IN    IRON. 


is  for  a  temperature  of  10°C.  ;  curve  II.  for  a  temperature  of 
670°C. ;  curve  III.  for  a  mean  temperature  of  about  742°C.  (it 
varied  a  few  degrees  during  the  observations) ;  and  curve  IV. 
for  a  mean  temperature  of  about  771°C.  In  Fig.  77  the  early 
portions  only  are  shown ;  the  scale  of  H  is  wide,  in  order  to 
display  well  the  crossing  of  the  curves. 


Fig.  78  shows  the 


Magnetising  Force  0-S. 


JljUW 

10,000 
9,000 
8,000 
7,000 
;J  6,000 

1    5,000 

ft, 
4,000 

3.0CO 
2,OCO 
1,000 

\ 

1 

\\ 

/ 

/ 

y 

-x  

* 

—  """* 

\ 

100 


200 


300  400 

Temperature. 


600 


600 


700    7S5fcOO*C 


FIG.  79.— Relation  of  Permeability  of  Temperature  in  Iron,  under  a 
Weak  Magnetising  Force. 


whole  process  of  magnetisation  (in  the  same  group  of  experi- 
ments) with  a  twenty-fold  smaller  scale  of  H.  The  rapid 
rise  and  low  apparent  saturation  value  in  curve  IV.,  where 
the  temperature  approaches  most  closely  to  the  critical  value, 
are  to  be  noted.  The  same  results  are  shown  in  a  different 
manner  in  Figs.  79,  80,  and  81,  also  copied  from  Hopkinson's 
paper.  These  give  the  permecMlity  /n  in  relation  to  the 


MAGNETISATION    OP   IRON    AT   VARIOUS    TEMPERATURES.       173 

temperature  for  three  specified  values  of  the  magnetising 
force  (0'3,  4'0,  and  45).  Fig.  79  shows  in  a  striking  way 
the  suddenness  with  which  susceptibility  to  small  magnetic 
force  is  lost  at  the  critical  point,  and  how  this  is  preceded 

Magne  f  ising  Force  4-Q 


Permeability  /ju 

X 

V 

X 

1 

1 

0  100  ZOO  300  4CO  500  600  700        785600G 

Temperature 

Fia.  80. — Relation  of  Permeability  to  Temperature  in  Iron,  under  a 
Moderate  Magnetising  Force. 

by  an  enormous  augmentation  of  susceptibility ;  the  other 
two  curves  show  how  much  more  gradual  is  the  passage  from 
the  magnetic  to  the  non-magnetic  state  when  we  have  to 
deal  with  stronger  forces.  In  the  curve  of  Fig.  79  the  perinea- 


500 


Magnetising  Force 45-0 


700        7 


0  TOO  ZQQ  300  400 

Temperature 

Fia.  81. — Relation  of  Permeability  to  Temperature  in  Iron,  under  a 
Strong  Magnetising  Force. 

bility  at  atmospheric  temperatures  is  367  ;  as  the  temperature 
rises  it  increases  at  first  slowly  and  afterwards  with  great 
rapidity,  reaching  the  maximum  already  mentioned  of  11,000 
at  775°. 

§  112.  Whitworth's  Mild  Steel.— Figs.  82  and  83  give  a 
corresponding  selection  of  Hopkinson's  results,  for  a  specimen 
of  mild  steel  contained  0-126  per  cent,  of  carbon.  Its  critical 
temperature  was  721°C.,  above  which  the  permeability  was 
only  1-12.  The  curves  reproduced  here  correspond  to  the 
following  temperatures  : — Curve  I.,  12°C.  ;  curve  II.,  about 
620°C.  -,  curve  III.,  about  715°C.  It  will  be  seen  that  these 


174 


MAGNETISM    IN    IRON. 


present  the  same  characteristics  as  the  corresponding  curves 
for  iron.     With  a  magnetising  force  of  0'3  the  highest  permea- 


Fia.  82. — Magnetisation  of  Mild  Steel  at  Various  Temperatures. 

bility  is  over  9,000,  and  this  is  found  at  a  temperature  only  a 
very  few  degrees  below  the  critical  point. 


40 


50 


20  30 

Magnetic  Force  H. 
FIG.  83.  —  Magnetisation  of  Mild  Steel  at  Various  Temperatures. 

§  113.  Whitworth's  Hard  Steel.  —  Fig.  84,  taken  from  the 
same  source,  relates  to  a  sample  of  hard  steel  containing  0-96 
per  cent,  of  carbon.  The  sample  was  annealed  before  the 
observations  were  made.  The  three  curves,  I.,  II.,  and  III., 
are  for  three  temperatures,  9°C.,  about  522°C.,  and  about 
678°C.  respectively.  Fig.  85  is  the  curve  of  //,  and  tempera- 
ture for  the  same  sample,  the  magnetising  force  being  1-5. 


MAGNETISATION  OP  NICKEL  AT  VARIOUS  TEMPERATURES.      175 

The  loss  of  magnetic  quality  at  the  critical  temperature  is 
scarcely  so  sudden  as  in  wrought  iron  and  mild  steel,  and  the 
influence  of  heating  is  more  uniformly  distributed  at  lower 
temperatures ;  but  the  same  general  characteristics  are  again 
obvious. 


10  20 

Magnetic  Force  H. 

Fia.  84.— Magnetisation  of  Hard  Steel  at  Various  Temperatures. 
Magnetising  Force  1-5. 


200  3UO  400 

Temperature. 


5UU 


600  700  C. 


Fia.  85. — Relation  of  Permeability  to  Temperature  in  Hard  Steel. 

§  114.  Hopkinson's  Experiments  with  Nickel. — In  dealing 
with  nickel,  Hopkinson*  has  pursued  the  same  method  of 
experiment,  using  a  ring,  and  finding,  by  the  ballistic  method, 
curves  of  magnetisation,  while  the  ring  was  maintained  at  one 

*  Proc.  Roy.  Soc.,  Vol.  XLIV.,  1888,  p.  317. 


176 


MAGNETISM    IN    IRON. 


or  another  of  a  series  of  temperatures  which  ranged  up  to  the 
critical  point  at  which  magnetic  susceptibility  disappears. 
The  specimen  tested  was  impure,  containing  95  per  cent,  of 
nickel,  with  about  1  per  cent,  (each)  of  iron,  cobalt,  and 
carbon,  and  1J  per  cent,  of  copper.  Its  critical  point  was 
about  310°C.  A  little  below  that  temperature  the  suscepti- 
bility diminished  very  rapidly  with  rise  of  temperature,  though 
there  was  no  such  excessively  rapid  loss  of  susceptibility 
as  iron  shows  (under  weak  magnetising  force)  when  the 


8,000 


2,500 


2.0CO 


1,500 


1,000 


29£fC. 


284°C. 


ufc 


10 


40  50 

Magnetic  Force  H, 


70 


FIG.  86. — Magnetisation  of  Nickel  at  Various  Temperatures. 


critical  point  is  approached.  At  lower  temperatures  the 
susceptibility  was  observed  to  increase  with  rise  of  temperature 
when  the  magnetic  force  was  low,  but  to  decrease  with  rise  of 
temperature  when  the  magnetic  force  was  high,  in  accordance 
with  what  has  been  already  described  as  characteristic  of  the 
effects  of  temperature  upon  all  the  magnetic  metals.  Thus, 
taking  curves  of  B  or  of  I  and  H  at  any  two  temperatures 
(both  well  below  the  critical  point)  it  is  found  with  nickel,  as 
with  iron,  that  the  curve  for  the  lower  temperature  lies  at 


MAGNETISATION  OF  NICKEL  AT  VARIOUS  TEMPERATURES.      177 

first  below  and  afterwards  above  the  other.  Figs.  86  and  87 
give  a  selection  of  Hopkinson's  curves.  In  Fig.  86  the  curves 
of  B  and  H  are  drawn  for  five  temperatures  :  one  is  an  ordinary 
atmospheric  temperature,  and  the  other  four  are  high  tempe- 
ratures tending  towards  the  critical  point.  At  the  first  of 
these  (245°C.)  there  is  a  marked  gain  of  susceptibility  for  forces 
lying  below  45  or  50.  The  whole  group  illustrates  well  how  the 
loss  of  magnetic  quality  supervenes  when  the  temperature  is 
sufficiently  raised. 

The  same  results  are  shown  in  a  different  manner  in  Fig.  87. 
There  the  induction   B  is  represented  as  a  function  of  the 


2,500 


m 


0       50      100      150      200      250      300   350°C. 
Temperature. 

FIG.  87.— Magnetisation  of  Nickel  at  Various  Temperatures. 


temperature — the  induction,  namely,  that  is  reached  when  the 
metal  is  magnetised  at  constant  temperature  by  the  application 
of  the  force  which  is  specified  separately  for  each  curve.  These 
curves  should  be  compared  with  the  curves  of  ju,  and  tempera- 
ture which  have  been  given  for  iron  and  steel  (Figs.  71 — 81, 
and  85). 

The  main  points  of  difference  in  the  magnetic  behaviour  of 
nickel  and  iron  with  respect  to  temperature  are,  that  in  nickel 
the  effects  of  temperature,  when  the  temperature  is  low,  are 
more  considerable  than  they  are  in  iron ;  that  in  nickel  the 


178  MAGNETISM    IN    IRON. 

critical  point  is  much,  lower;  and  that  in  nickel  the  change 
from  the  magnetic  to  the  non-magnetic  state  is  much  less 
abrupt  than  in  iron.  Perhaps  for  this  reason  the  change  is 
not  associated  with  any  such  striking  physical  changes  as  ac- 
company it  in  iron.  Nickel  does  not  recalesce,  and  an  experi- 
ment of  Hopkinson's*  shows  that  the  change  from  the  non- 
magnetic to  the  magnetic  state,  as  the  metal  cools,  is  attended 
by  no  sudden  liberation  or  absorption  of  heat.  Notwithstand- 
ing the  fact  that  the  specimen  tested  by  Hopkinson  was 
not  pure  the  critical  point  found  with  it  appears  to  be  fairly 
representative  of  the  critical  point  in  nickel.  In  another 
sample  tested  by  du  Bois,f  the  critical  point  again  occurs 
about  300°C. 


§115.  Effects  of  Temperature  within  the  Atmospheric 
Range. — None  of  the  three  magnetic  metals  is  sufficiently 
affected  by  temperature  to  have  its  magnetic  susceptibility 
very  materially  altered  by  any  change  of  temperature  that 
is  liable  to  be  experienced  within  the  atmospheric  range.  In 
the  case  of  iron,  especially,  the  effects  which  atmospheric 
fluctuations  of  temperature  exert  upon  the  magnetic  qua 
lity  are  too  slight  to  require  to  be  taken  account  of  in 
specifying  the  magnetic  properties  of  a  sample,  or  in  stating 
the  results  of  experiments.  Even  when  iron  is  raised  to 
100°C.  the  influence  of  the  heating  is  by  no  means  consider- 
able. This  is  shown  in  Fig.  88,  which  gives  two  pairs  of 
curves  of  I  and  H,  one  referring  to  iron  wire  in  the  soft 
annealed  state,  and  the  other  to  the  same  wire  after  it  had 
been  hardened  by  stretching  beyond  the  limit  of  elasticity .| 
The  full  line  in  each  pair  is  a  curve  of  magnetisation  taken 
at  atmospheric  temperature  (7°  or  8°C.  in  this  case),  and 
the  dotted  line  is  a  curve  of  magnetisation  taken  while 
the  wire  was  maintained  at  a  temperature  of  100°C.  by 
enclosing  it  in  a  tube  through  which  a  current  of  steam 
was  kept  up.  The  curves  cross  at  much  the  same  value 
of  I  for  both  conditions  of  the  metal,  though  at  very  different 
values  of  H. 

*  Hopkinson,  loc.  cit.t  *  319.        t  Du  Bois,  Phil.  Mag.,  April,  1890. 
J  Ewing,  Phil,  Trans.,  1885,  p.  637. 


\ 


8* 


to 

I 


<JOij&$/jdu6ew 


180  MAGNETISM   IN   IRON. 

§  116.  Effects  of  Varying  Temperature,  the  Magnetic  Force 
being  Constant. — In  the  experiments  which  have  been  noticed 
above,  the  temperature  was  kept  constant  and  the  magnetic 
force  was  varied.     If  we  keep  the  force  constant  and  vary  the 
temperature,  a  rather  complex  series  of  effects  will  be  observed. 
In  the  first  place,  there  is  in  general  an   effect  which  is  not 
reversible — that  is  to  say,  which  would  not  be  undone  if  the 
temperature  were  brought  back  to  its  initial  value.     The  first 
effect  of  any  heating  is  like  the  effect  of  vibration :  it  produces 
a  permanent  change  in  the  magnetisation ;  but  whether  that 
change  will  be  an  increase  or  a  decrease  will  depend  on  the 
previous  history  of  the  magnetised  piece.     The  reason  of  this 
should  be  apparent  when  we  come  to  discuss  molecular  theories 
of  induced  magnetism :  in  effect  it  is   this,  that  at  any  (not 
extreme)  stage  in  the  process  of  magnetisation  there  are  groups 
of  molecules  verging  on  instability,  which  are  precipitated  into 
instability  when   the   temperature   begins   to   change.      This 
effect  is  distinct  from — and  may  be  much  greater  than — the 
reversible  changes  of  magnetism  which  are  caused  by  alternate 
heating  and  cooling.     But  when  any  alternation  of   heating 
and  cooling  is   sufficiently  often  repeated,  a  cyclic  regime  is 
established ;    the    magnetism    will    then    fluctuate    between 
two  values,  but  whether  the  higher  or  the  lower  value  will 
correspond  to  the  hotter  state  will  depend  on  whether  the 
magnetism  is  below  or  above  a  certain  value.  In  other  words,  the 
effects  of  temperature,  when  tested  in  this  way  (by  repeated  alter- 
nate heating  and  cooling),  become  reversed  when  the  magnetisa- 
tion is  sufficiently  strong.    When  there  is  but  little  magnetisa- 
tion heating  augments,  and  cooling  reduces   the  amount  of 
magnetism,  whether  that  be  either  residual  or  induced  by  the 
action  of  a  constant  magnetising  force ;  when  there  is  much 
magnetisation   the   reverse    happens.      The  reversal  of  effect 
which  is  observed  in  experiments  of  this  class  is  evidently  to 
be  anticipated  in  connection  with  the  crossing  of  the  magneti- 
sation curves  in  experiments  of  the  class  described  above.    But, 
on   account  of  complications  proceeding   from   magnetic  hys- 
teresis, it  is  not  possible  to  infer,  from  results  of  experiments 
of  the  one  kind,  where  the  reversal  should  occur  in  the  other. 

That  the  first  effect  of  any  change  of  temperature  on  the 
magnetism  of  iron  or  steel  is  not  reversible  has  been  shown  by 


EFFECTS    OP    VARYING   TEMPERATURE.  181 

many  experiments,  probably  first  by  those  of  Wiedemann.* 
If  the  magnetism  that  is  dealt  with  is  residual,  and  there  is 
no  acting  magnetic  force,  a  cyclic  process  of  heating  and  cooling, 
or  of  cooling  and  heating,  results  in  a  reduction  of  the  mag- 
netism.    If,  on  the   other  hand,  the  magnetism  that  is  dealt 
with  is  that  which  has  been  reached  by  applying  a  magnetising 
force  which  is  kept  in  action  while  the  temperature  is  changed, 
then  a  cyclic  process  of  heating  and  cooling  or  of  cooling  and 
heating  results  in  an  increase  of  magnetism.     In  either  case  it 
is,  in  general,  only  after  many  repetitions  of  the  temperature 
cycle  that  the  change  of  magnetism  becomes  cyclic.     In  the 
earliest  cycles  we  find,  superposed  upon  what  may  be  called 
the  legitimate  or  differential  variations  of  magnetism,  a  pro- 
gressive shaking  in  of  magnetism   if   that  is  induced,   or  a 
progressive  shaking  out  of  magnetism  if  that  is  residual.     It 
is  in  the  first  cycle  that  this  is  most  conspicuous,  but  it  can 
often  be  traced  in  the  second  and  even  in  later  cycles.     By 
repeating  the  temperature  cycle  often  enough  we  may  get  rid 
of  these  progressive  changes,  and  may  then  study  the  differential 
effects  of  heating  and  cooling.     One  or  two  experiments  of  this 
class  will  be  briefly  referred  to. 

§  117.  Experiments  in  Alternate  Heating  and  Cooling  of 
Magnetised  Iron. — In  the  first  of  thesef  a  hardened  iron  wire 
was  tested,  surrounded  by  a  tube,  on  which  a  magnetising  coil 
was  wound,  and  through  which  currents  of  steam  or  of  cold  water 
could  be  alternately  passed.  The  resulting  magnetic  changes 
were  observed  by  means  of  a  magnetometer.  The  wire  was  at 
first  demagnetised,  and  then  from  time  to  time  its  magnetism 
was  increased  a  step  by  passing  a  weak  current  through  the 
magnetising  coil ;  but  after  each  such  step  the  current  was 
stopped,  and  the  only  force  in  action  was  the  vertical  com- 
ponent of  the  earth's  field.  The  first  series  of  heatings  and 
coolings  (between  100°C.  and  6°C.)  made  I  fluctuate  between 
about  2-U  (cold)  and  2'23  (hot).  At  this  stage  heating 
increased  I.  Later  the  fluctuations  of  I  were  from  3'51 
(cold)  to  3-56  (hot);  the  effect  still  had  the  same  sign. 
Later  still  it  became  reversed ;  the  fluctuations  of  I  were 
between  8'69  (cold)  and  8-67  (hot);  and  later  still  the 

*  "  Galvanisms,"  II.,  §  522  et  seq.    t  Ewing,  Phil  Trans.,  1885,  p.  633. 


182  MAGNETISM  IN  IRON 

reversed  effect  was  more  marked,  the  range  being  from  9*09 
(cold)  to  9-04  (hot). 

A  similar  experiment  with  a  piece  of  annealed  iron  wire* 
showed  that  the  reversal  of  effect  took  place  in  that  case  when 
I  was  about  20.  At  an  early  stage  I  ranged  from  4*77  (at 
6°C.)  to  4-95  (at  100°C.) ;  at  a  later  stage  (after  reversal)  I 
ranged  from  37'53  (at  6°C.)  to  about  36-77  (at  100°C.).  In 
both  cases  the  reversal  occurred  at  a  very  early  point  in  the 
process  of  magnetisation. 

In  another  case  f  the  magnetisation  of  the  specimen  was 
examined  at  intermediate  points,  during  heating  and  during 
cooling,  to  see  whether  there  was  hysteresis  in  the  relation  of 
magnetism  to  temperature.  The  specimen — a  long  iron  wire — 
was  fixed  inside  a  glass  tube  which  could  be  connected  at  one 
end  to  any  one  of  three  small  boilers  capable  of  supplying  a 
steady  current  of  steam,  of  alcohol  vapour,  and  of  sulphuric 
ether  vapour,  or  to  a  cistern  supplying  cold  water.  Steam  and 
cold  water  (at  14°C.)  were  alternately  passed  through  the  tube 
many  times  until  the  magnetic  state  of  the  wire  was  observed 
to  change  from  one  to  the  other  of  two  nearly  steady  values. 
Then  readings  of  the  magnetometer  were  taken  during 
the  passage  through  the  tube  of  (1)  cold  water,  (2)  ether 
vapour,  (3)  alcohol  vapour,  (4)  steam,  (5)  alcohol  vapour, 
(6)  ether  vapour,  (7)  cold  water.  This  completed  a  cycle 
of  temperature  changes  in  which  two  intermediate  points 
(35°C.  and  78J°C.)  were  fixed  during  the  process  of  heating 
and  cooling.  The  method  was  adopted  in  order  to  secure 
that  the  iron  should  be  exposed  sufficiently  long  to  an  atmo- 
sphere of  definite  temperature  to  give  it  time  to  take  that 
temperature  throughout,  and  so  avoid  any  possibility  of 
error  proceeding  from  the  sluggishness  with  which  changes  of 
temperature  take  place.  The  stream  of  vapour  was  kept  up  in 
every  case  until  the  magnetometer  reading  became  steady. 

The  iron  was  magnetised  to  begin  with  sufficiently  strongly  to 
make  the  heating  cause  a  diminution  and  the  cooling  cause 
an  augmentation  of  magnetism.  The  only  magnetic  force  in 
action  during  the  heating  and  cooling  was  the  earth's  vertical 
field.  In  the  following  statement  of  observed  results  the 

*  Loc.  cit.  p.  635.  t  Loc.  cit.,  p.  631. 


EFFECTS    OF   VARYING    TEMPERATURE. 


numbers    are   proportional    (on    an    arbitrary   scale)    to    the 
intensity   of   magnetisation.     The  arrows  show  the  sequence 


of  the  changes 


Temp. 


Water. 
U°C. 
17,416 
17,418 


Ether 

vapour. 

35°C. 

17,382 

17,382 


Alcohol 
vapour. 
78*°C. 
17J304 
17,304 


Steam. 
100°C. 
17,262 


The  whole  change  was  about  0-9  per  cent,  of  the  whole 
magnetism.  It  is  clear  from  the  readings  at  35°C.  and  78J°C. 
that  the  changes  occurred  without  any  perceptible  hysteresis  ; 
the  magnetisation  at  intermediate  points  was,  as  nearly  as  can 
be  judged,  the  same  during  heating  as  during  cooling. 


Magnetic  Moment  of  Bar 
(in  arbitrary  units) 

1  1  |__J  1  .  1  ! 

* 

*y[ 

% 

S^ 

•" 

s 

, 

X 

^ 

^ 

^ 

V 

X 

^ 

Ss 

^ 

^ 

\ 

\ 

'    10      Z 

3      J 

3       40       SO      60       7 

3      50      5^?     /^       110     120    130     /40    150     60 

Temperature,  Degrees  C. 
Fia.  89.— Effects  of  Heating  and  Cooling  a  Steel  Bar  Magnet. 

Fig.  89  shows  the  result  of  another  experiment  of  the  same 
class,*  in  which  a  steel  bar  magnet  was  heated  and  cooled  in  a 
bath  of  oil,  through  a  considerably  wider  range  of  temperature 
(between  10°C.  and  158°C.).  The  temperature  of  the  oil  was 
altered  very  slowly — so  slowly  that  it  took  more  than  1 7  hours 
to  complete  the  cycle  of  changes  shown  in  the  figure — in  order 
to  let  the  bar's  temperature  be  sensibly  uniform  with  that  of 

*  Loc.  cit.,  p.  638. 


184  MAGNETISM    IN    IRON. 

the  oil,  which  was  observed  by  means  of  two  thermometers. 
Several  heatings  and  coolings  preceded  the  cycle  in  which  the 
observations  were  made.  Here,  as  in  the  former  case,  there 
was  no  sensible  hysteresis  in  the  relation  of  magnetism  to 
temperature. 

§  118.  Hysteresis  in  the  Relation  of  Magnetic  Suscep- 
tibility to  Temperature. — Although  no  hysteresis  appears  in 
the  experiments  which  have  just  been  described — the  magnetic 
condition  depending,  apparently,  only  upon  the  actual  tempe- 
rature and  not  upon  past  temperatures — it  is  still  possible  to 
experiment  under  conditions  which  show  hysteresis  in  the  rela- 
tion of  magnetic  quality  to  temperature.  Hysteresis  of  this 
kind  is  found  when  the  range  through  which  the  temperature 
varies  is  sufficiently  wide  to  include  the  critical  region  in  which 
magnetic  quality  disappears  during  heating  and  reappears 
during  cooling.  The  disappearance  and  reappearance  do  not 
occur  at  the  same  temperature.  There  are  two  critical  tem- 
peratures :  one  is  the  point  at  which  magnetic  quality  is  lost 
during  heating,  and  this  is  higher  than  the  other,  namely,  the 
point  at  which  magnetic  quality  is  regained  during  cooling. 

In  ordinary  iron  and  steel  the  difference  between  these  two 
critical  temperatures  is  not  great — perhaps  ten  or  twelve 
degrees  in  soft  iron — and  the  direct  measurement  of  it  is  a 
matter  of  some  difficulty.  That  there  is  a  difference,  however, 
admits  readily  of  easy  experimental  proof,*  and  may,  indeed, 
be  inferred  from  the  phenomenon  of  recalescence.  It  is  known 

*  A  very  pretty  experiment,  showing  that  the  change  of  state  which 
iron  or  steel  undergoes  in  passing  a  red  heat  occurs  at  different  tempera- 
tures during  heating  and  during  cooling,  has  been  described  by  Mr. 
H.  F.  Newall  (Phil.  Mag.,  June,  1888),  and  also  (Rep.  Brit.  Assoc., 
1889,  p.  517 ;  Proc.  Roy.  Dublin  Soc.,  1886)  by  Mr.  F.  T.  Trouton. 
A  lamp  flame,  held  under  an  iron  or  steel  wire  (which  is  in  circuit 
with  a  galvanometer),  so  that  a  short  portion  of  the  wire  becomes  red 
hot,  is  made  to  travel  slowly  under  the  wire,  and  it  is  found  that  a 
current  appears  in  the  galvanometer,  the  direction  of  the  current 
depending  on  the  direction  in  which  the  flame  travels.  The  current  is 
due  to  difference  in  thermo-electric  quality  between  that  part  of  the 
iron  which  has  changed  its  state  by  passing  the  critical  point  and  that 
part  which  has  not  changed  its  state,  and  depends  on  the  fact  that  on  the 
side  which  is  being  heated  the  change  of  state  is  occurring  at  a  higher 
temperature  than  on  the  side  which  is  being  cooled. 


HYSTERESIS    WITH    RESPECT    TO    TEMPERATURE.  185 

that  in  recalescence  there  is,  superposed  upon  the  process  of 
cooling,  a  real  rise  in  temperature,  and  it  is  known  that  the 
change  of  magnetic  state  occurs  simultaneously  with  the  recal- 
escence. If  the  change  of  constitution  which  then  takes  place 
depended  upon  the  actual  temperature  alone,  and  not  upon 
preceding  temperatures,  this  rise  in  temperature  would  be  im- 
possible, for  it  would  undo  the  very  change  which  causes  it.  To 
make  it  possible,  the  altered  state  of  the  material  must  be 
able  to  stand  some  elevation  of  temperature  without  changing 
back  again;  in  other  words,  the  change  of  constitution  must 
show  hysteresis  with  respect  to  temperature. 

Osmond,*  who  has  made  a  very  full  investigation  of  the 
temperatures  at  which  perturbations  take  place  during  the  pro- 
cesses of  heating  and  cooling,  finds  that  with  electrolytically 
deposited  iron  there  is  a  marked  evolution  of  heat  during 
cooling,  about  855°C.,  and  a  marked  absorption  of  heat  during 
heating,  about  867°C.  There  is  no  reason  to  doubt  that  it  is 
at  and  about  these  temperatures  that  the  changes  from  the 
non-magnetic  to  the  magnetic  state  and  from  the  magnetic  to 
the  non-magnetic  state  respectively  occur. 

In  hard  steel  Osmond's  experiments  show  a  wider  difference 
between  the  two  critical  temperatures.  The  principal  evolu* 
tion  of  heat  during  cooling  occurs  at  674°C.,  and  the  corre- 
sponding absorption  of  heat  during  heating  occurs  at  705°C. 
At  any  temperature  between  these  limits  we  should  expect  to 
find  this  steel  magnetic  if  the  immediately  preceding  tempera- 
ture had  been  lower,  but  non-magnetic  if  the  immediately 
preceding  temperature  had  been  higher. 

A  much  more  remarkable  difference  of  the  same  kind  is  found 
in  what  is  called  nickel-steel.  Hopkinson  has  examined  severaJ 
alloys  of  iron  and  nickel,  and  has  discovered,  by  direct  mag, 
netic  tests,  that  in  some  of  them  the  metal  may  retain  either  a 
magnetic  or  a  non-magnetic  condition  throughout  an  extra- 
ordinarily wide  range  of  temperature.!  His  results  as  to 
other  physical  properties  of  these  alloys,  as  well  as  their  mag- 
netic properties,  are  of  the  highest  interest. 

*  Osmond,  "  Transformations  du  fer  et  du  carbone,"  Memorial  de 
I'Artillerie  de  la  Marine,  1888. 

t  Hopkinson,  Proc.  Boy.  Soc.,  December  12,  1889  ;  January  23,  1890 ; 
May  1,  1890. 


186 


MAGNETISM    IN    IRON. 


§  119.  Hopkinson's  Experiments  with  Nickel-Iron  Alloys.— 
The  samples  were  tested  ballistically,  in  the  form  of  rings,  the 
temperature  being  inferred  from  the  resistance  of  the  secondary 
coil.  A  sample  containing  4'7  per  cent,  of  nickel  and  0'22  per 
cent,  of  carbon  gave  a  magnetisation  curve,  at  the  temperature 
of  the  atmosphere,  resembling  the  curves  given  by  ordinary 
mild  steel.  When  this  specimen  was  heated,  the  magnetic 
quality  being  tested  by  reversals  of  a  magnetising  force  of 
0-12  C.-G.-S.,  it  was  found  to  lose  susceptibility  as  the 
temperature  approached  800°C.,  and  not  to  regain  it  on 
cooling  until  the  temperature  had  fallen  to  650°C.  or 
600°C.  Fig.  90  shows  the  changes  which  took  place  during 
heating  and  cooling;  it  gives  the  induction  B  produced 
by  reversing  the  force  H  of  O12,  in  terms  of  the  tempera- 
ture. It  will  be  seen  that  there  is  a  clear  range  of  about 


<fOU 

200 
ISO 
100 

so 
n 

* 

c 
.0 

y\ 

| 

^ps 

^ 

\  ^ 

•x  

—  *-x 

-N  *--*• 

V 

—  !_.. 

1  — 

V^_ 

*•-.    1  

+-m 

s 

=-  —  I  —  ^ 

•500 
Fra.  90.— Steel  with  4'7  per  cent.  Nickel.     Magnetising  Force  012. 

150  degrees  within  which  the  metal  may  exist  in  either  of 
two  states :  in  one  state  it  is  as  susceptible  as  ordinary  mild 
steel ;  in  the  other  it  is  practically  non-magnetisable,  the 
permeability  being,  in  fact,  only  about  1*4.  Under  stronger 
magnetising  forces  the  magnetic  quality  appears  and  dis- 
appears at  about  the  same  two  points.  Further,  an  experiment 
in  which  the  time  rates  of  heating  and  of  cooling  were  observed 
showed  that  the  same  two  temperatures  were  marked  by 
perturbations  such  as  occur  at  the  critical  temperature  in  iron, 
the  higher  temperature  being  associated  with  an  absorption  of 
heat  in  the  process  of  heating,  and  the  lower  temperature 
with  an  evolution  of  heat  in  the  process  of  cooling.  The  heat 
which  was  liberated  in  cooling,  at  the  temperature  where 


NICKEL-IRON    ALLOYS. 


187 


magnetic  quality  returned,  was  found  to  be  about  150  times  the 
quantity  which  would  raise  the  temperature  of  the  piece  by 
one  degree. 

Still  more  striking  results  were  obtained  by  Hopkinson  with 
a  specimen  containing  25  per  cent,  of  nickel.     This  was  non- 


300 


0  100      I       ZOO  300  400      '       500       '  600  C 

Fia.  91.— Steel  with  25  per  cent.  Nickel.    Magnetising  Force  6'7. 

magnetisable  at  ordinary  temperatures  in  its  primitive  state,  but 
on  being  cooled  in  a  freezing  mixture  it  became  magnetisable  at  a 
temperature  a  little  below  the  freezing  point.  Kendered  mag- 
netisable in  this  way,  it  retained  its  magnetic  quality  on  being 


4000 

c 

,<?<W 

1  ^ 

,  —  -> 

"N 

2000 

^     \ 

^ 

woo 

0 

\ 

', 

1 

\ 

—  1  —  ^ 

1-  - 

—  \  — 

*     1-  —  — 

—  1  — 

\ 

\}  \ 

500 
FIG.  92.— Steel  with  25  per  cent.  Nickel.     Magnetising  Force  64. 

warmed  until  the  temperature  rose  to  5SO°C.  At  that  tem- 
perature it  became  again  non-magnetisable,  and  remained  so 
on  cooling  down  to  the  ordinary  temperature  of  the  air.  Within 
a  range  of  about  600  degrees  this  steel  is  capable  of  existing, 
quite  stably,  in  either  state.  Figs.  91  and  92  show  the 


188 


MAGNETISM    TN    IRON. 


induction  B  (produced  by  reversals  of  magnetic  forces  equal  to 
6*7  and  64  respectively)  in  terms  of  the  temperature.  In  the 
non-magnetisable  state  the  permeability  is  only  1*4;  in  the 
magnetisable  state  the  permeability  resembles  (but  falls  rather 
short  of)  that  of  hard  nickel.  The  curve  of  magnetisation  (at 
13°C.)  is  copied  in  Fig.  93.  Hopkinson  has  also  shown  that 
other  physical  properties  of  this  alloy  change  along  with  its 
magnetic  properties.  The  electrical  conductivity  is  markedly 
different  in  the  two  states :  at  0°C.,  for  instance,  the  specific 
resistance  is  only  0*00052  if  the  substance  has  been  brought 
into  its  magnetisable  state  by  applying  a  freezing  mixture,  but 
is  0*00072  if  it  has  been  brought  into  the  non-magnetisable 
state  by  previous  heating  above  600°C. 


/r/1/1/5 

ir—  — 

-*-- 

41000 
3.000 

onnn 

o 

-d 
o 

^—  -* 

~^~~ 

,—  — 

1 

^ 

^ 

^ 

£ 

/ 

1000 

y 

/ 

*^ 

Magi 

tf/V's/ 

nq    / 

'orct 

0        10      20      30      40      50     60      ID     80     90     100     110'     120    130  140 
Fia.  93.— Steel  with  25  per  cent.  Nickel.     Curve  of  B  and  H. 


Equally  pronounced  differences  are  found  with  regard  to 
extensibility  and  strength.  In  the  non-magnetisable  state  this 
metal  is  comparatively  soft ;  wires  show  an  elongation  of  30 
per  cent,  or  more  before  rupture,  and  break  with  a  load  of  about 
50  tons  per  square  inch.  In  the  magnetisable  state  it  is  much 
harder ;  there  is  only  7  or  8  per  cent,  of  extension,  and  the 
strength  is  as  much  as  85  tons  per  square  inch,  or  even  more. 
"  If,"  says  Hopkinson,  "  this  material  could  be  produced  at  a 
lower  cost  these  facts  would  have  a  very  important  bearing. 
As  a  mild  steel  the  non-magnetisable  material  is  very  fine,  having 
so  high  a  breaking  stress  for  so  great  an  elongation  at  rupture. 
Suppose  it  were  used  for  any  purpose  for  which  a  mild  steel 
is  suitable  on  account  of  this  considerable  elongation  at  rupture: 


NICKEL-IRON    ALLOTS. 


189 


if  exposed  to  a  sharp  frost  its  properties  would  be  completely 
changed — it  would  become  essentially  a  hard  steel  until  it 
had  actually  been  heated  to  a  temperature  of  600° C."  It  is 
interesting  to  notice  that  specimens  of  the  non-magnetisable 
metal  when  broken  in  the  testing  machine  pass  into  the  mag- 
netisable  state ;  the  change  occurs  along  with  the  mechanical 
hardening  which  the  metal  suffers  in  being  drawn  out. 

This  remarkable  power  of  assuming  one  or  other  of  two 
widely  different  physical  states  is  less  noticeable  when  the  per- 
centage of  nickel  in  the  alloy  is  further  increased.  Two  other 
nickel- iron  alloys,  containing  respectively  30  per  cent,  and 


0  50  tOO  150  200          250  U 

FIG.  94.— Steel  with  33  per  cent.  Nickel.    Magnetising  Force  I'O. 


33  per  cent,  of  nickel,  Hopkinson  found  to  be  much  more 
permeable,  and  to  show  very  much  less  hysteresis  with  respect 
to  temperature  in  changing  between  the  magnetisable  and 
non-magnetisable  states,  and  to  change  at  a  comparatively  low 
temperature.  Fig.  94  shows  the  results  of  magnetising  the 
33  per  cent,  sample  with  a  force  H  of  I'O.  The  curves,  which 
correspond  to  rising  and  falling  temperatures,  are  not  far  apart, 
and  the  change  takes  place  at  temperatures  lying  near  200°C. 
In  the  30  per  cent,  sample  the  critical  temperatures  are  lower 
(about  140°C.  in  heating  and  125°C.  in  cooling).  Finally,  a 
sample  containing  73  per  cent,  of  nickel  showed  no  material 


190  MAGNETISM   IN   IRON. 

difference  between  the  critical  points  for  heating  and  cooling ; 
its  critical  temperature  was  600°C. 

These  observations  suggest  the  idea  that  a  substance  such 
as  manganese  steel,  which  is  nearly  non-magnetic  in  all 
conditions  of  temperature  in  which  it  has  hitherto  been  tested, 
would  become  magnetic  if  the  temperature  were  sufficiently 
lowered.  And  it  is  even  possible  that  other  metals  than  iron, 
nickel,  and  cobalt  are  non-magnetic  only  because  all  our 
dealings  with  them  are  at  temperatures  above  a  "critical 
point."  This  conjecture,  however,  is  not  borne  out  by 
experiment,  so  far  as  observations  at  low  temperature  have  yet 
been  made.  Even  at  the  very  low  temperature  of  liquid  air 
there  is  no  development  of  magnetic  quality  in  metals  which 
are  non-magnetic  under  ordinary  conditions. 

§119a.  Researches  on  Effects  of  Temperature  by  Dr.  Morris. 
— A  very  complete  investigation  of  the  immediate  effects  of 
heating  on  the  magnetic  qualities  of  certain  specimens  of  iron 
has  been  made  by  Dr.  D.  K.  Morris,*  who  has  examined  both 
the  permeability  and  the  hysteresis  over  a  range  of  temperature 
extending  considerably  beyond  the  critical  point.  The  specimens 
were  in  the  form  of  rings,  electrically  heated  by  means  of  a 
non-inductive  coil  of  platinum  wire. 

Under  small  magnetising  forces  (H  <  0-5  C.G.S.)  the 
permeability  was  found  to  rise  with  rising  temperature,  at  first 
slowing,  and,  then,  in  the  neighbourhood  of  300°C.  quite 
rapidly.  It  remained  nearly  constant  between  400°  and  500° 
and  then  rose  with  very  great  rapidity  as  the  temperature 
approached  7509,  reaching  a  value  of  nearly  13,000.  After 
this  it  fell  off  with  equal  rapidity  as  the  critical  point  was 
reached.  The  critical  point  was  at  795°s  780°  and  770°  in 
three  specimens  examined  by  Dr.  Morris. 

Changes  of  a  generally  similar  kind  were  observed  in  the 
fermeability  with  respect  to  stronger  forces.  In  all  cases  the 
general  rise  in  permeability,  with  rising  temperature,  is  subject 
to  several  set-backs  at  temperatures  below  the  critical  point. 
These  are  illustrated  in  Fig.  94A,  which  is  copied  from  one  of 
the  curves  in  Dr.  Morris'  paper.  It  shows  the  changes  which 

*  Morris,  Phil.  Mag.,  September,  1897. 


CRITICAL   POINTS    IN    IRON. 


191 


are  observed  in  the  maximum  permeability  as  the  Iron  is  heated. 
The  curve  passes  at  least  three  maximums  before  the  critical 
point  is  reached.  Even  above  the  chief  critical  point  some 
susceptibility  to  magnetisation  is  still  found  :  between  800° 
and  1,000°C.  there  is  another  maximum,  and  after  falling  to  a 
value  of  only  about  2'3,  about  750°C.,  the  permeability  again 
begins  to  increase  very  appreciably  as  the  temperature 
continues  to  rise. 

It  is  clear  that  these  irregular  changes  of  magnetic  quality 
which  begin  as  low  as  250°C.  or  even  lower,  and  go  on  to  1000°C. 
or  higher,  and  of  which  the  great  drop  at  the  chief  critical 


Fia.  94A. — Effects  of  Temperature  on  the  Permeability  of  Iron  (Morris). 

point  is  only  a  particular  case,  are  associated  with  changes  in 
crystalline  structure  of  which  we  have  independent  evidence. 
Sir  W.  Roberts  Austen  has  examined  the  rate  of  cooling  of  iron, 
from  a  bright  red  heat,  and  has  found  corresponding  irregu- 
larities, due  to  the  evolution  of  heat  within  the  substance  of  the 
metal  at  a  series  of  stages  in  the  cooling  process.  Fig.  94s  is 
a  record  of  one  of  his  results,*  the  co-ordinates  representing 

*  Fifth  Report  of  the  Alloys  Research  Committee,  Proc.,  Inst.  Mech. 
Eng.,  February,  1899 


192 


MAGNETISM    IN   IRON. 


temperature  and  time. 
As  the  iron  cools  a 
series  of  more  or  less 
sudden  evolutions  of 
heat  occur  due  to  some 
internal  convulsion.  The 
lowest  of  these  occurs 
at  obout  260°C.,  the 
highest  (in  the  dia- 
gram) at  about  900°. 
On  comparing  the  two 
curves,  Fig.  94s  and 
Fig.  94A,  we  can  readily 
trace  a  connection  be- 
tween the  changes  of 
structure  which  the 
cooling  curve  exhibits 
and  the  changes  of 
magnetic  quality,  not 
only  at  the  great  mag- 
netic critical  point  (say 
770°C.),  but  also  at  the 
earlier  and  later  points 
of  arrest. 

With  regard  to  hy- 
steresis, Dr.  Morris'  ex- 
periments show  that 
with  constant  limits  of 
magnetic  induction  the 
area  enclosed  within 
cyclic  curves  of  B  and 
H  becomes  enormously 
reduced  as  the  tempera- 
ture approaches  the  chief 
critical  point :  in  other 
words  the  hysteresis 
tends  in  great  part  to 
disappear.  He  gives  the 
following  figures  for  a 


AGEING       OF   IRON. 


193 


specimen  of  iron,  previously  annealed  at  a  temperature  of 
1150°C.,  and  then  taken  through  cvcles  of  magnetisation 
between  the  limits  B=  ±4550: — 


Temperature. 
°C. 

Hysteresis  in 
Ergs  per  cub.  cm. 
per  Cycle 
(B=±4550). 

Temperature. 
°C. 

Hysteresis  in 
Ergs  per  cub.  cm. 
per  Cycle 
(B=±4550). 

18 

137i 

249 
352 
457 
554 

613 
555 
508 
475 
379 
335 

634 

695 
730 
748 
764£ 

264 
178 
128 
109 
81 

§119b.  "Ageing"    of   Iron    by    Prolonged     Exposure    to 
Moderate  Temperature. — Apart  from   the  immediate  change 
which  heating   produces   in  the  magnetic  quality  of  iron  it 
brings  about   a  slow  deterioration  of  the  metal  which  shows 
itself  in  reduced  permeability  and  increased  hysteresis.     This 
action  proceeds  very  gradually  if  the  temperature  is  compara- 
tively low.     An  important  practical  instance  of  it  is  found  in 
transformers.     The  heat  which  is  generated  in  the  transformer 
by  the  currents  in  the  coils  and  by  hysteresis  in  the  core  keeps 
the  apparatus  at  a  temperature  considerably  higher  than  that 
of  its  surroundings.     It  was  observed   that  the  efficiency  of 
transformers  generally  became  reduced  after  they  had  been  at 
work  for  some  months,  and   this  was  traced  to  increase   of 
hysteresis  in  the  core.*     At  first  it  was  conjectured  that  this 
increase  of  hysteresis  was  a  species  of  "  fatigue  "  due  to  repeated 
reversals  of  magnetisation,  resembling  the  fatigue  of  an  elastic 
body  under  repeated  reversals  of  mechanical  strain,  but  it  was 
shown  by  the  author  that  reversals  of  magnetism  did  not  in 
themselves   have   any   such   effect.!      Mr.    W.   M.    MordeyJ 
showed  conclusively  that  the  augmentation  of  hysteresis  arose 
simply  from   prolonged  heating.      More  recently  the  subject 
has  been  investigated  by  Mr.  S.  R.  Roget,  who  has  examined 

*  Curves  illustrating  this  increase  were  published  in  The  Electrician  by 
Mr.  G.  W.  Partridge,  Dec.  7,  1894. 
t  The  Electrician,  Dec.  7,  1894,  and  Jan.  11,  1895. 
£  Mordey,  Proc.  Roy.  Soc.,  June,  1895. 

0 


194 


MAGNETISM    IN    IRON. 


the  effect  of  prolonged  exposure  to  temperatures  ranging  from 
50°C.  to  700°C.*  Even  so  low  a  temperature  as  50°C.,  if  con- 
tinued  for  some  weeks,  produces  an  appreciable  effect.  When  the 
temperature  was  160°C.  the  hysteresis  of  a  specimen  of  trans- 
former iron  increased  so  rapidly  that  in  a  few  hours  it  doubled, 
and  in  a  few  days  it  reached  nearly  three  times  its  original 
value.  But  a  longer  time  of  heating  at  such  a  temperature 
as  that  makes  the  hysteresis  pass  a  maximum  and  begin  to 
diminish  again,  though  not  sufficiently  to  revert  to  the  value 
it  had  before  heating. 


FIG.  94c.  —Effects  of  Baking  of  the  Hysteresis  of  Sheet  Iron  (Roget). 

The  tables  opposite,  which  are  quoted  from  Mr.  Roget'a 
paper,  show  how  a  maximum  of  hysteresis  is  passed  under 
continued  exposure  to  a  constant  temperature,  at  least  in  cases 
where  the  temperature  is  not  less  than  135°C. 

The  second  table  deals  with  higher  temperatures,  ranging  from 
300°  to  700°C.,  and  there  it  will  be  observed  that  the  maximum 
is  reached  after  a  very  short  time — in  some  cases  after  a  few 
minutes.  In  both  tables  the  hysteresis  is  stated  for  a  cycle 
with  the  limits  B  =  ±  4000. 

^  *  Koget,  Proc.  Roy,  Soc.,  May  12,  1898,  and  Dec,  8  1898, 


AGEING"    OF   IRON. 


195 


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196 


MAGNETISM    IN    IRON. 


These  changes  of  hysteresis  are  associated  with  changes  of 
permeability  in  the  early  portion  of  the  magnetisation  curve. 
The  figures  94c  and  94o  illustrate  this  by  showing  the 
hysteresis  cycle  and  also  the  early  stage  of  the  B-H  curve 
for  a  specimen  :  first  in  its  initial  state,  then  after  heating  at 
200°C.  for  19  hours,  and  finally  after  heating  at  the  same 


1,000 


0  '5         1-0          1-5         2-0         2'5         8'5 

FIG.  94D.— Effects  of  Baking  on  the  Permeability  of  Sheet  Iron  (Roget). 

temperature  for  four  days,  by  which  time  the  maximum  of 
hysteresis  had  been  passed. 

It  is  a  characteristic  of  these  changes  that  they  occur 
Irregularly,  and  they  are  much  more  conspicuous  in  some 
specimens  of  iron  than  in  others.  Specimens,  especially  of 
sheet  steel,  will  sometimes  be  found  in  which  prolonged  heating 
is  almost  without  effect,  but  the  conditions  which  secure  this 
very  desirable  result  are  not  fully  understood. 


CHAF.TER    IS. 


EFFECTS   OF   STRESS. 

§  120,  Effects  of  Stress :  Introductory. — No  part  of  our 
subject  is  more  interesting  than  that  which  deals  with  the 
effects  of  mechanical  stress  in  altering  the  susceptibility,  the 
retentiveness,  and  other  qualities  of  the  three  magnetic  metals. 
The  matter  is  not,  at  least  as  yet,  one  of  practical  moment,  for 
it  has  at  present  no  direct  bearing  on  any  of  the  applications  of 
magnetism ;  but  its  importance  on  the  theoretical  side  is  not 
easily  overrated.  The  effects  of  stress  form  a  fascinating  subject 
of  inquiry  to  the  physical  student,  and  are  likely  to  play  a  con- 
siderable part  in  revealing  the  molecular  structure  which  makes 
magnetisation  possible.  The  subiect  is  a  large  one,  and  the 
results  that  have  been  already  obtained  are  too  intricate  to 
permit  more  than  a  very  general  account  of  them  to  be  given 
here.  It  will  be  most  convenient  to  state  the  salient  facts, 
without  much  regard  to  the  historical  order  of  their  discovery. 
The  first  inquirer  in  this  field  appears  to  have  been  Matteucci,* 
who  noticed  an  increase  of  magnetism  in  a  magnetised  iron 
bar  when  the  bar  was  pulled  lengthwise.  Villari  f  made  the 
important  discovery  that  the  character  of  this  effect  became 
reversed  when  the  bar  was  sufficiently  strongly  magnetised : 
let  the  iron  bar  be  weakly  magnetised,  and  the  effect  of  pull 
is  to  increase  the  magnetism ;  but  let  the  bar  be  strongly 
magnetised,  and  the  effect  of  pull  is  to  reduce  the  magnetism. 
This  "Villari  reversal"  (as  it  is  now  called)  of  the  mag- 
netic effects  of  stress  in  iron  was  rediscovered  by  Lord 
Kelvin  in  the  course  of  an  inquiry  which  may  be  said  to  have 

*  Comptes  Rendus,  1847  ;  Ann.  de  Chemie  et  de  Physique,  1858. 
f  Pogg.  Ann.,  1868. 


198  MAGNETISM  IN  IRON. 

laid  the  foundation  of  exacb  knowledge  in  this  subject.* 
Kelvin  studied  the  effects  of  longitudinal  stress  by  loading  and 
unloading  if  on  wire  and  steel  wire  in  magnetic  fields  of  various 
strengths ;  he  extended  the  same  method  of  investigation  to 
nickel  and  cobalt.  He  found  by  experiment  with  a  steel  gun- 
barrel  under  hydraulic  pressure  that  the  effects  of  transverse 
stress  were  opposite  in  kind  to  those  of  longitudinal  stress.  Com- 
paring the  results  of  longitudinal  and  transverse  pull,  he  pointed 
out  that  the  effect  of  a  simple  pulling  or  pushing  stress  was 
to  develop  a  difference  of  magnetic  susceptibility  in  directions 
lying  along  and  across  the  line  of  pull  or  push ;  and  he  applied 
this  consideration  to  the  case  of  torsional  strain,  deducing 
results  which  were  verified  by  experiment,  and  discussing  earlier 
experiments  by  Wiedemann,  who,  it  may  be  added,  has  made 
the  relations  of  torsion  and  magnetisation  the  subject  of  much 
detailed  study. t  The  work  of  Kelvin  has  been  followed  up 
and  extended  by  others,  particularly  in  the  direction  of  inves- 
tigating the  forms  which  the  magnetisation  curve  (the  curve  of 
I  and  H)  assumes  when  the  piece  under  test  is  subjected  to 
various  kinds  and  degrees  of  stress ;  and  also  of  investigating, 
by  continuous  magnetometric  observations,  the  manner  in  which 
a  loaded  piece  gradually  acquires  or  loses  magnetism  when  the 
loads  are  varied,  a  constant  magnetising  force  being  kept  in 
action.  The  effects  of  hysteresis,  which  present  themselves  at 
every  turn  in  experiments  on  this  subject,  do  much  to  compli- 
cate the  results  :  and  it  is  only  by  following  both  methods  of 
inquiry — that  is  to  say,  by  examining  the  consequences  of 
changing  the  magnetic  force  while  the  state  of  stress  is  kept 
constant,  and  also  those  of  changing  the  stress  while  the  mag- 
netic force  is  kept  constant — that  we  can  obtain  a  tolerably  clear 
connected  view  of  the  phenomena. 

§  121.  Effects  of  Longitudinal  Pull  on  the  Susceptibility 
and  Retentiveness  of  Nickel. — It  is  most  convenient  to 
begin  with  nickel,  because  the  effects  of  stress  are — for  the 

*  Lord  Kelvin  "  Effects  of  Stress  on  Magnetisation,"  forming  Parts 
VI.  and  VII.  of  his  great  series  of  Papers  on  the  "  Electro-Dynamic  Qua- 
lities of  Metals "  (Phil.  Trans.,  1875,  1878  ;  Eeprint  of  Papers,  Vol.  II., 
pp.332— 407). 

t  See  Wiedemann's  Elektricitat,  Vol.  III.,  §  762,  et  seq. 


EFFECTS    OF   PULL   IN    NICKEL. 


199 


most  part — much  greater  in  it  than  in  the  other  metals, 
and  are  also  simpler  in  one  very  material  respect.  There 
is  nothing  in  nickel  that  corresponds  to  the  Villari  reversal 
in  iron.  If  we  apply  pull  to  a  magnetised  rod  or  wire 
of  nickel,  we  find — as  Kelvin  first  showed* — that  pull 
diminishes  the  magnetism,  and  relaxation  of  pull  increases  the 
magnetism;  and  this  effect  is  still  observed,  however  strongly 
or  weakly  the  piece  be  magnetised. 

If  we  magnetise  nickel  while  it  is  kept  in  a  state  of  longi- 
tudinal tension  by  means  of  a  constant  load,  we  find  an  enor- 
mous reduction  in  its  susceptibility.  This  is  well  shown  by 
the  curves  of  Fig.  95,  which  show  the  magnetisation  of  a  long 
piece  of  annealed  nickel  wire  under  various  amounts  of  longi- 
tudinal pull.f  The  wire  was  O'OGScm.  in  diameter,  and  374 
diameters  long ;  its  section  was  0'363  sq.  mm.,  so  that  each 
kilogramme  of  load  produced  a  stress  of  275  kilogrammes  per 
sq.  mm.  The  curves  drawn  in  full  lines  show  the  relation 
of  I  to  H  when  there  was  no  load,  and  also  when  the  load  was 
2  and  12  kilogrammes,  corresponding  to  5*5  and  33  kilos,  per 
sq.  mm.  respectively.  The  effect  of  tensile  stress  in  depressing 
the  magnetisation  curve  is  very  marked.  With  no  load  the 
maximum  susceptibility  is  fully  15,  with  2  kilos,  it  is  only 
about  8,  and  with.  12  kilos,  the  resistance  to  magnetisation  has 
become  so  great  that  the  maximum  of  susceptibility  has  not 
been  reached  even  by  raising  H  to  100  C.-G.-S. 

Great  as  the  effects  of  stress  are  upon  the  magnetic  suscepti- 
bility, they  are  even  greater  on  the  retentiveness.  In  the  same 
figure  (95),  three  other  curves  have  been  drawn  in  broken  lines, 

thus : ,  to  show  the  residual  magnetism  that  was 

found  on  withdrawing  H  at  each  of  a  series  of  stages  during 
the  process  of  magnetising  under  each  load.  The  presence  of 
load  reduces  the  residual  magnetism  even  more  than  it  reduces 
the  total  induced  magnetism.  The  residual  value  of  I,  after 
applying  a  force,  H,  of  100,  is  nearly  300  when  there  is  no 
stress;  under  2  kilos,  it  is  reduced  to  150;  and  under  12 

*  Reprint  of  Papers,  Vol.  II.,  p.  382. 

t  This  and  a  number  of  the  succeeding  figures  are  taken  from  two 
papers,  on  the  "  Magnetic  Qualities  of  Nickel "  (Phil.  Trans.,  1888,  pp.  325 
and  333),  in  one  of  which  the  author  had  the  collaboration  of  Mr.  Q.  C. 
Cowan. 


202  MAGNETISM    IN    IRON. 

kilos,  it  is  only  16.  The  proportion  of  residual  to  total  induced 
magnetism  Las  a  maximum  o£  076  under  no  load  ;  but  under 
2  kilos,  it  is  reduced  to  0'61,  and  under  12  kilos,  to  O19.  The 
amounts  of  magnetism  which  disappear  when  H  is  removed, 
under  various  loads,  form  a  greater  proportion  of  the  whole 
the  more  the  load  is  increased,  although  (owing  to  the  re- 
duction in  the  total  magnetism)  the  absolute  amount  that 
disappears  when  a  strong  force  is  removed  is  greater  for  a 
small  load  than  it  is  for  no  load,  and  then  less  again  for  a  large 
load.* 

The  presence  of  a  small  amount  of  load  may,  therefore, 
be  said  to  increase  the  susceptibility  of  nickel  with  respect  to 
that  part  of  the  magnetism  which  comes  and  goes  when  H 
is  alternately  applied  and  removed,  provided  H  is  strong; 
when  H  is  weak  the  effect  of  any  load  is  only  to  reduce  this 
susceptibilty. 

Fig.  96  gives  the  results  of  a  similar  experiment  in  which 
the  same  piece  of  nickel  wire,  after  being  hardened,  how- 
ever, by  a  slight  amount  of  stretching  beyond  its  limit  of 
elasticity,  was  magnetised  under  a  succession  of  pulling  loads, 
ranging  up  to  18  kilos.,  or  about  50  kilos,  per  sq.  mm.  With 
no  load  the  maximum  susceptibility  of  this  hardened  wire  was 
about  8.  Under  the  highest  load  the  susceptibility  was  prac- 
tically constant  within  the  range  of  H  used  (up  to  100  C.-G.-S.), 
and  its  value  was  only  about  0'5  (permeability  about  6 -3).  In 
this  condition  of  stress  the  residual  magnetism  is  almost 
nil.  The  dotted  lines  in  this  figure  show  the  effect  of 
gradually  removing  the  strongest  value  of  H  which  had  been 
reached  in  the  process  of  magnetising;  they  illustrate  well 
how  the  residual  magnetism  becomes  smaller,  not  only  abso- 
lutely, but  as  a  fraction  of  the  whole  magnetism,  when  heavier 
loads  are  used. 

§  122.  Effects  of  Longitudinal  Push  on  the  Susceptibility 
and  Retentiveness  of  Nickel. — The  reduction  of  susceptibility 
and  retentiveness  in  nickel  by  longitudinal  tensile  stress  is  asso- 
ciated with  an  equally  striking  augmentation  of  susceptibility 

*  This  fact  has  been  noticed  independently  and  commented  on  in  a  recent 
Paper  by  H.  Tomlinson  (Phil.  Mag.,  May,  18GO). 


EFFECTS  OF  PUSH  IN  NICKEL.  203 

and  retentiveness  by  longitudinal  compressive  stress.  Fig.  97 
shows  an  arrangement  by  which  nickel  rods  have  been  tested,* 
under  compression,  within  a  yoke  of  wrought  iron,  by  means  of 
the  method  described  in  §  58,  the  total  magnetisation  being 
determined  ballistically  by  reversing  H,  and  the  residual  mag- 
netisation by  deducting  the  ballistic  effect  got  by  removing  H 
from  half  the  ballistic  effect  got  by  reversing  H.  The  influ- 
ence of  a  number  of  loads  was  examined,  ranging  up  to  19 '8 
kilos,  per  sq.  mm.  Every  addition  of  load  produced  a  decided 
increase  of  susceptibility,  and  caused  an  increasing  fraction  of 


Fia.  97. — Arrangement  for  Testing  the  Magnetisation  of  Metals  under 
Compression. 


the  whole  magnetism  to  be  retained  on  the  withdrawal  of  the 
magnetising  force,  until  finally,  under  the  heaviest  load,  the 
magnetisation  curve  rose  with  remarkable  steepness,  and  the 
maximum  proportion  of  residual  to  total  induced  magnetism 
reached  the  astonishingly  great  value  of  0'96.  In  this  group 
of  experiments  the  nickel  rod  was  in  a  hard  (unannealed) 
state. 

The  results  of  the  observations  are  shown  in  Figs.  98 
and  99. 

Fig.  98  gives  the  induced  magnetism  I  in  terms  of  H,  under 
each  amount  of  longitudinal  compressive  stress ;  and  Fig.  89 

*  Phil.  Trans.,  1888,  A,  p.  333. 


204 


MAGNEXltiM    IN    IKON. 


7 


BFFECTS    OF    STRESS    IN    NICKEL. 


205 


206 


MAGNETISM    IN   IRON. 


gives  the  residual  magnetism,  which  was  observed  in  the  usual 
way  by  withdrawing  H  at  a  number  of  stages  during  the 
taking  of  each  magnetisation  curve.  Especially  to  be  noted  is 
the  sharpness  with  which  the  curve  of  induced  magnetism,  under 
the  heaviest  stresses,  bends  over  when  H  is  about  20.  The 
approach  towards  saturation  is  extremely  rapid,  and  the  change 
from  a  highly  susceptible  state  to  an  insusceptible — because 
nearly  saturated — state  is  remarkably  abrupt. 

Fig.   100  shows  the  result  of  the  same  experiment   in   a 
different  way  :    the  permeability  //,  is  plotted  there  in  relation 


woo 


2GQO  3000  4-300 

Maantfic    Induction    B. 


FIQ.  100.— Permeability  of  Nickel  in  the  Lard  state. 

to  B  for  three  conditions  of  stress  which  are  specified  on  the 
curves. 

Fig.  101  records  a  corresponding  set  of  observations  made  on 
a  nickel  rod  in  the  annealed  state,  under  compressive  stresses 
ranging  up  to  6 '8  kilos,  per  square  mm.  The  curves  of  p  and 
B  which  relate  to  this  experiment  have  already  been  shown  in 
Fig.  41,  §  75. 

§  123.  Effects  of  Cyclic  Variation  of  Longitudinal  Stress  on 
the  Magnetism  of  Nickel. — As  might  be  anticipated  from  the 
curves  that  have  been  given  above,  a  magnetised  nickel  wire 
subjected  to  cyclic  variations  of  pull  by  loading  and  unloading 


EFFECTS  OF   STRESS   IN    NICKEL. 


207 


208 


MAGNETISM    IN    IRON. 


it  with  suspended  weights  suffers  much  reduction  of  its  mag- 
netism when  the  weights  are  put  on,  and  much  increase  of  its 
magnetism  when  the  weights  are  taken  off.  This  happens 
whether  the  magnetism  be  induced  or  residual. 

Iu  Fig.  102  a  number  of  curves  are  drawn  to  show  the 
observed  effect  (upon  I)  of  applying  and  removing  loads  while 
the  magnetising  force  specified  in  the  right-hand  margin  of  the 
figure  remained  continuously  in  action.  The  dotted  curves 
in  the  same  figure  show  how  the  residual  magnetism 


iro 

Ruidual  MarllS 


e          a 

Load    in    Kilos. 

Fio.  102.— Effects  of  Loading  and  Unloading  Nickel  Wire  in  Various 
Constant  Fields. 


which  was  left  after  the  action  of  the  strongest  force 
(116  C.-G.-S.)  was  affected  by  loading  and  unloading.  In 
this  experiment  each  kilogramme  of  load  corresponds  to 
a  stress  of  2 '7 5  kilos  per  square  mm.  When  these  curves 
are  compared  with  corresponding  curves  for  iron,  which  will  be 
given  later,  it  will  be  seen  that  there  is  comparatively  little 
hysteresis  of  magnetism  with  respect  to  stress  in  these. 

There  is,  however,  some  hysteresis;  the  curve  for  the 
process  of  loading  invariably  lies  above  the  curve  for  the 
process  of  unloading,  even  when  the  cyclic  variations  of  stress 


EFFECTS    OF   PULL   IN    IRON.  209 

are  repeated  often  enough  to  make  the  magnetic  changes  become 
strictly  cyclic.  With  hardened  nickel  wire,  tested  under  a 
wider  range  of  stresses,  there  is  even  less  hysteresis  than  here.* 

§  124.  Effects  of  Longitudinal  Pull  in  Iron. — Turning  now 
to  iron,  we  find  that  much  more  complex  variations  of  mag- 
netic quality  are  produced  by  longitudinal  stress.  We  have 
to  distinguish  between  two  cases,  that  of  soft  annealed  iron, 
and  that  of  iron  which  has  beeri  hardened  by  a  mechanical 
operation  such  as  stretching,  which  has  given  it  a  permanent 
set.  With  hardened  metal  the  effects  of  stress  are  in  general 
much  greater  than  with  annealed  metal.  Both  cases  have  thia 
in  common,  that  the  presence  of  any  moderate  amount  of  longi- 
tudinal pull  increases  the  susceptibility  when  the  magnetisation 
is  weak,  but  reduces  the  susceptibility  when  the  magnetisation 
is  strong.  We  have  here  the  phenomenon  of  the  Villari  reversal 
to  which  allusion  has  already  been  made.  But  in  the  case  of 
hard  metal,  where  it  is  possible  to  apply  a  stronger  pull  with- 
out permanently  altering  the  characteristics  or  structure  of  the 
piece,  it  appears  that  the  presence  of  a  sufficiently  great 
amount  of  stress  may  be  unfavourable  to  magnetisation,  even 
in  the  earliest  stages  of  the  magnetising  process.  These,  as 
well  as  other  effects  of  stress,  will  be  best  appreciated  by  means 
of  a  careful  study  of  curves  which  exhibit  the  process  of  mag- 
netisation in  iron  wires  pulled  by  various  amounts  of  hanging 
load.  The  wires,  in  the  experiments  to  be  described,  were  of 
such  a  size  that  each  kilogramme  of  load  corresponded  to  a 
stress  of  about  2*2  kilogrammes  per  square  mm. 

§  125.  Annealed  Iron  under  Pulling  Stress.— Fig.  103 
shows,  by  curves  of  I  and  H,  the  magnetisation  of  a  wire  of 
soft  annealed  iron  under  various  amounts  of  longitudinal  pull 
(no  load,  2  kilos,  and  6  kilos),  f  The  curve  for  no  load  lies  at 
first  lowest,  and  finally  highest.  Each  curve,  in  fact,  lies  at 
first  lower,  and  afterwards  higher,  than  a  curve  for  any  greater 
amount  of  load.  Thus,  the  presence  of  load  is  favourable  to 
magnetisation  when  I  is  small,  but  unfavourable  when  I  is  great. 
And  the  curves  obtained  by  removing  the  magnetising  force 
(which  are  shown  to  the  left  in  the  figure)  preserve  throughout 
their  whole  course  the  relative  places  with  which  they  start, 

*  Phil.  Trans.,  1888,  A,  p.  331.      t  Ewing,  Phil.  Trans.,  1885,  plate  64. 


210 


MAGNETISM    IN    IRON. 


tne  differences  between  them  becoming  only  accentuated  as  the 
magnetising  force  is  reduced  to  zero.  Thus,  the  presence  of 
pulling  load  is  unfavourable  to  the  residual  magnetism  left 


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Fio.  103.  —  Magnetisation  of  Annealed 
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EFFECTS   OF  PULL   IN   SOFT   IRON. 


211 


after  a  strong  field  has  been  applied;  though,  as  another 
experiment  has  shown,  it  is  favourable  to  the  residual  mag- 
netism that  is  left  after  magnetisation  by  a  weak  field.  Its 


GOO 


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FIG.  104.— Magnetisation  of  Annealed  Iron  under  Various  Amounts  of 
Longitudinal  Pull. 

P2 


212  MAGNETISM    IN    IRON. 

influence  on  the  residual  magnetism  is,  in  fact,  of  the  same 
kind  as  its  influence  on  the  induced  magnetism;  both  suffer 
reversal  when  the  magnetisation  is  sufficiently  increased.  The 
curves  of  residual  magnetism  (which  are  not  drawn  in  the  figure) 
cross  each  other  in  the  same  manner  as  the  curves  of  induced 
magnetism.  The  results  of  this  experiment  are  shown  in  a  differ- 
ent manner  in  Fig.  104.  A  series  of  curves  are  drawn  there,  each 
relating  to  a  particular  value  of  the  force  H,  to  show  the  relation 
of  the  value  of  I  reached  by  applying  that  force,  to  the  amount 
of  load  which  was  present  when  the  force  was  applied. 

This  figure  shows  very  clearly  that,  except  under  the  strongest 
magnetising  force  that  was  applied  in  the  experiment,  the  pre- 
sence of  a  very  small  amount  of  pulling  load  increases  the  sus- 
ceptibility ;  and  further,  that  except  in  the  weakest  fields,  the 
presence  of  a  fairly  large  amount  of  pulling  load  reduces  the  sus- 
ceptibility. Except  at  very  low  and  again  at  high  magnetisations, 
there  is  maximum  of  a  susceptibility  occurring  with  a  particular 
load;  and  the  value  of  this  load  becomes  smaller  as  the  magnetisa- 
tion is  increased.  This  maximum  disappears  in  the  lowest  fields, 
no  doubt  only  because  the  load  is  insufficiently  great  to  show  it. 

§  126.  Hardened  Iron  under  Pulling  Stress. — Figs.  105  and 
106  show  the  effects  of  various  amounts  of  longitudinal  pull  on 
iron  wire  which  had  been  previously  hardened  by  stretching 
beyond  the  elastic  limit.  Fig.  105  gives  the  induced  magnet- 
ism, and  Fig.  106  gives  the  residual  magnetism,  both  in  relation 
to  H,  the  process  of  magnetising  being  performed,  as  in  previous 
examples,  while  a  constant  load  hung  from  the  wire. 

The  first  thing  to  observe  here  is  the  immense  effect  which  a 
moderate  amount  of  pull  has  in  augmenting  the  susceptibility 
with  respect  to  feeble  magnetising  forces.  On  the  other  hand, 
when  a  condition  approaching  saturation  is  reached,  the  presence 
of  load  is  unfavourable  to  magnetisation ;  in  other  words,  we 
have,  as  before,  the  Villari  reversal.  But  it  is  now  to  be  noticed 
that  even  in  the  weakest  fields  the  susceptibility  is  increased 
only  when  the  amount  of  the  load  is  moderate :  to  apply  stress 
beyond  a  certain  amount  is  prejudicial,  whether  the  magnetisa- 
tion be  strong  or  weak.  This  is  shown  by  the  fact  that  the 
curve  for  14*8  kilos  lies  below  the  curves  for  5  and  10  kilos 
thoughout  its  whole  course. 


EFFECTS   OF   PULL    IN   HARD 


213 


The  same  remarks  apply  to  the  residual  magnetism  (shown 
(n  Fig.  106).    The  influence  of  stress  on  it  is  even  greater. 
Fig.  107  shows,  in  the  same  way  as  Fig.  104,  the  results  of 


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Fia.  105.— Magnetisation  of  Hardened  Iron  under  various  amounts  of 
Longitudinal  Pull. 


214 


MAGNETISM   IN   IRON. 


Fio.  106.— Residual  Magnetisation  of  Hardened  Iron  under  varioui 
amounts  of  Longitudinal  Pull. 


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FIG.  107.—: 


Magnetisation  of  Hardened  Iron  under  various  amounts    of 
Longitudinal  Pull. 


216  MAGNETISM    IN   IRON. 

another  experiment  of  the  same  kind,  in  which  a  piece  of  the 
same  iron  wire,  also  hardened  by  stretching,  was  magnetised  under 
a  series  of  loads  which  in  this  case  ranged  up  to  about  19  kilos. 
This  figure  shows  very  clearly  that  a  moderate  amount  of  load  is 
more  favourable  to  magnetisation  than  either  less  load  or  more ; 
the  exact  amount  which  is  most  favourable  depends  on  the 
degree  of  magnetisation,  being  less  in  strong  fields  than  in  weak 
ones.  It  varies,  in  this  example,  from  about  10  to  5  kilos,  for 
the  range  of  magnetic  forces  with  which  the  experiment  deals. 
The  effects  of  pulling  stress  on  the  susceptibility  of  steel  are 
generally  similar  to  the  effects  in  iron. 

§  127.  Effects  of  Applying  Longitudinal  Pull  to  Magnetised 
Iron. —  In  the  experiments  described  above  the  pull  was  applied 
before  magnetisation  began,  and  was  then  left  constant.  It 
remains  to  describe  what  is  observed  when  the  pull  is  varied 
while  the  magnetising  force  is  kept  constant.  If  there  were  no 
hysteresis,  we  should  obtain  in  this  way  curves  similar  to  those 
of  Figs.  104  or  107.  In  consequence  of  hysteresis  the  changes 
of  magnetism  that  are  actually  produced  by  changing  the  load, 
though  maintaining  a  general  similarity  to  these  curves,  differ 
from  them  in  two  important  respects.  In  the  first  place,  the 
initial  effects  which  are  observed  when  we  first  begin  to  change 
the  stress  are  in  general  very  great,  and  are  to  be  distinguished 
from  the  effects  obtained  after  a  cycle  of  stress  changes  has  been 
repeated  once  or  twice.  These  initial  effects  of  applying  stress 
resemble  those  that  are  produced  by  vibration,  although  the 
process  of  loading  may  be  conducted  in  such  a  way  that  no 
actual  vibration  takes  place.  They  proceed,  as  the  molecular 
theory  to  be  discussed  later  indicates,  from  a  condition  of  mole- 
cular instability  ;  and  they  do  not  disappear  when  the  stress  is 
removed.  Thus,  when  we  begin  for  the  first  time  to  load  an  iron 
wire,  to  which  a  weak  or  moderately  strong  magnetising  force 
has  been  applied,  we  find  that  the  first  loads  are  associated  with 
an  increase  of  magnetism,  which  may  be  so  great  as  to  increase 
the  whole  quantity  ten-fold.  Moreover,  if  a  load  has  been 
hanging  from  the  wire  while  the  magnetising  force  was  being 
applied,  we  find  that  on  beginning  to  remove  it  an  increase  of 
induced  magnetism  takes  place.  Again,  if  we  are  dealing  with 
residual  magnetism,  the  first  effect  of  changing  the  load  after 


EFFECTS    OF   VARYING    THE   PULI>  217 

the  magnetising  force  has  been  removed  (whether  by  way  of  in- 
creasing or  decreasing  the  load)  is  in  general  to  reduce  largely 
the  amount  of  the  residue.  It  is  only  after  applying  and 
removing  any  load  several  times  that  the  magnetic  effects  of 
the  stress-changes  become  cyclic — that  is  to  say,  after  several 
repetitions  of  the  operation,  the  magnetism  will  be  found  to 
alter  from  one  to  another  of  two  definite  values  when  the  load 
is  put  on  and  when  it  is  taken  off.  But  even  then  the  effects 
of  hysteresis  are  manifest ;  for  any  intermediate  value  of  the 
load  is  found  to  be  associated  with  very  different  values  of 
the  magnetism  during  loading  and  during  unloading.  These 
features  are  well  seen  when  we  examine  curves  drawn  to  show 
the  changes  of  magnetism  in  relation  to  the  changes  of  load, 
of  which  Figs.  108  and  109  are  examples.*  They  refer  to 
an  iron  wire,  hardened  by  previous  stretching  beyond  its  elastic 
limit,  of  such  a  size  that  each  kilo  of  load  corresponds  to 
a  stress  of  about  2 '3  kilos  per  sq.  mm.  The  cycle  of  stress 
consisted  in  applying  and  removing  15  kilos. 

Beginning  at  the  bottom  of  Fig.  108,  at  the  point  marked  a, 
we  have  the  wire,  free  from  any  load  and  previously  demagnet- 
ised by  reversals,  exposed  to  a  magnetising  force  of  0*34:  C.-G.-S. 
In  this  state  there  was  very  little  magnetisation.  Then  loads 
were  applied,  and  the  effects  of  the  first  application  and  removal 
are  shown  by  the  dotted  lines  a  b  c.  The  full  lines  imme- 
diately above  them  show  the  effects  of  the  second  application 
and  removal  of  load,  by  which  time  the  magnetic  changes  had 
become  nearly  cyclic.  It  is  clear  that  in  the  first  loading  we 
have  to  deal  with  a  progressive  augmentation  of  magnetism 
superposed  on  cyclic  changes  of  the  character  shown  by  subse- 
quent cycles  of  loading — that  is  to  say,  we  have  an  initial  effect 
superposed  on  the  cyclic  effect. 

Next,  the  wire  was  demagnetised,  and  then  a  stronger  field 
(2-49  C.-G.-S.)  was  applied,  while  there  was  no  load.  The 
effects  of  the  first  loading  in  this  field  were  enormous ;  they 
are  shown  by  the  dotted  line  which  starts  from  the  point  d 
in  the  figure.  Here,  again,  a  repetition  of  the  process  of 
loading  and  unloading  brought  the  magnetic  changes  into  a 
nearly  cyclic  state,  which  is  shown  by  the  full  lines  at  the  top 
of  the  figure. 

*  Ewing,  PhU.  Trans.,  1885,  plate  63,  p.  603. 


218 


MAGNETISM    IN    IRON. 


Next,  a  stronger  field  still  (18-65  C.-G.-S.)  was  applied 
(Fig.  109).  The  curve  for  first  loading  still  shows  a  consider- 
able permanent  augmentation  of  magnetism  j  but  a  cyclic  state 


1 


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ffuts 


Loadin  Itdos 
Fio.  108.— Effects  of  applying  Pull  to  Magnetised  Iron. 

Is  reached  sooner  than  in  weaker  magnetic  fields.      In  still 
stronger  magnetic  fields  the  curves  become  more  and  more 


HYSTERESIS    IN   EFFECTS    OF    STRESS. 


219 


flattened  down  into  a  form  in  which  the  application  of  load 
causes  a  diminution  of  magnetism  throughout. 

Finally,  to  show  how  the  residual  magnetism  is  affected  by 
change  of  stress,  the  residue  left  after  applying  a  field  of  2  '49 
units  and  subjecting  the  wire  to  loads  in  that  field,  was  made  the 
subject  of  the  experiment  shown  by  the  lines  f  g  Ji  in  Fig.  108. 
These  curves  show  how  (starting  from  the  point/)  the  residual 
magnetism  suffered  changes  due  to  loading  and  unloading, 
which  may  best  be  described  as  a  progressive  decrease  of  mag- 


G  8  10 

Load  in  "kHai 
FIG.  109.— Effects  of  applying  Pull  to  Strongly  Magnetised  Iron. 

netism  superposed  upon  cyclic  changes  of  the  same  character  as 
those  which  are  shown  in  previous  figures.  If  we  repeat  the 
cycles  of  load  on  a  piece  in  which  there  is  only  residual  mag 
netism,  we  find,  in  fact,  cyclic  changes  of  the  same  general  kind 
as  those  that  are  found  when  a  magnetising  force  is  in  action. 

§  128.  Hysteresis  in  the  Effects  of  Stress. — The  hysteresis 
of  magnetism  with  respect  to  changes  of  load,  which  is  clearly 
exhibited  by  these  curves,  is  static  in  character — that  is  to 
say,  it  does  not  depend  on  the  time-rate  at  which  loads  are 


220 


MAGNETISM    IN   IRON. 


applied  nor  on  the  intervals  which  are  allowed  to  elapse  before 
readings  of  the  magnetisation  are  taken.  After  any  condition 
of  load  is  reached,  the  magnetism  does  not  change  with  the 
lapse  of  time,  except  possibly  to  a  very  insignificant  extent. 

During  each  loading,  after  a  cyclic  condition  has  been  estab- 
lished the  magnetism  is  at  first  increased ;  but  a  maximum  is 


Load  in  kilos. 

Fia.  110.— Effects  of  Pull  on  a  Stretched  Iron  Wire. 

passed  as  more  load  is  added,  and  later  additions  of  load  reduce 
the  magnetism.  A  similar  maximum  is  seen  during  unloading ; 
but  owing  to  hysteresis  the  maximum  comes  at  different  loads 
in  the  two  cases ;  each  maximum  is  shifted,  through  hysteresis, 
to  a  later  place  in  the  operation  than  it  would  otherwise  have. 


EFFECTS  OF  CYCLES  OF  STKESS. 


221 


Another  manifestation  of  hysteresis  is  seen  in  the  easy  gradient 
with  which  each  curve  begins,  as  the  process  of  loading  is 
changed  to  that  of  unloading,  or  vice  versd.  In  a  weak  field  the 
initial  gradient  of  each  curve  is  so  small  that  the  curve 
appears  to  set  out  tangent  to  the  line  of  loads. 

Fig.  110  may  be  referred  to  in  further  illustration  of  the 
presence  of  hysteresis  in   changes  of  magnetism   caused   by 


Load  in  kilos. 
Fio.  111. — Influence  of  Vibration  on  Effects  of  Loading  and  Unloading. 

changes  of  load.*  It  shows  the  effect  of  superposing  on  a 
principal  cycle  of  pulling  stress  changes  several  minor  cycles, 
in  each  of  which  hysteresis  is  very  apparent.  The  order  in 
which  the  loads  were  applied  was  this : — 0,  5,  0,  8,  3,  12'6, 
9,  12-6,  3,  8,  0.  The  wire  dealt  with  here  was  of  iron,  and 
had  been  hardened  by  stretching :  it  hung  in  a  constant  field 
the  force  of  which  was  0-34  C.-G.-S. 


222  MAGNETISM    IN   IRON. 

§  129.  Influence  of  Vibration  on  the  Effects  of  Stress. — 
These  indications  of  hysteresis  disappear  almost  entirely  if  we 
submit  the  piece  under  test  to  mechanical  vibration  either 
during  or  after  the  changes  of  load.  As  modified  by  vibration 
the  curves  for  loading  and  unloading  become  nearly  coincident. 
The  whole  amount  of  magnetic  change  is  increased.  A  maxi- 
mum point  is  still  found,  which  lies,  as  regards  load,  between 
the  two  maximums  that  are  observed  when  the  processes  are 
gone  through  without  vibration.  Tapping  the  wire  at  any 
stage  in  the  process  produces,  in  general,  a  large  change  in  its 
magnetism ;  but  if  loading  or  unloading  is  then  resumed, 
without  further  tapping,  the  presence  of  hysteresis  is  at  once 
conspicuous.  Fig.  Ill  (page  209)  illustrates  the  influence  of 
vibration,  by  showing  the  curves  got  by  repeated  loading  and 
unloading  of  an  iron  wire,  suspended  in  a  weak  magnetic  field, 
first  without  vibration,  and  also  with  smart  vibration  before 
each  reading  of  the  magnetometer  was  taken. 

§  130.  Effects  of  Loading  Annealed  Iron. — On  applying 
loads  to  an  annealed  iron  wire  hanging  in  a  magnetic  field,  we 
find  at  first  the  same  extreme  sensitiveness,  the  result  of  mole- 
cular instability.  ^Repetition  of  the  loading,  if  repeated  often 
enough,  brings  about  a  cyclic  state  in  which  there  is  much 
less  total  change  of  magnetism  than  is  found  in  the  corre- 
sponding experiment  with  hardened  metal.  As  to  the  character 
of  the  change,  it  depends  on  the  magnitude  of  the  load.  With 
a  sufficiently  light  load,  loading  produces  increase  and  unload- 
ing produces  decrease  of  magnetism  ;  with  a  moderately  heavy 
load  these  effects  are  reversed.* 

§  131.  Effects  of  Longitudinal  Stress  in  Cobalt. — Lord 
Kelvin,  testing  a  cobalt  bar  hung  vertically  in  the  earth's 
magnetic  field,  found  that  pulling  decreased  and  relaxing 
the  pull  increased  the  induced  magnetism.  The  effects  of 

*  For  examples  of  the  curves  got  by  loading  and  unloading  annealed  iron 
see  Phil.  Trans.,  1885,  plates  62  and  64.  Many  of  the  effects  of  stress, 
both  in  annealed  and  in  hardened  metal,  will  be  found  exhibited  there,  by 
means  of  curves,  more  completely  than  it  is  possible  to  exhibit  them  here. 
A  few  examples  of  the  effects  of  compressive  stress  on  the  curves  of  I  and 
H  for  iron  will  be  found  in  a  paper  in  the  Phil.  Mag.  for  September,  1888. 
The  presence  of  compressive  stress  lowers  the  curve,  as  might  be  antici- 
pated from  the  raising  of  it  by  tensile  stress,  shown  in  Figs.  103  and  105. 


EFFECTS    OF    STRESS    IN    COBALT. 


223 


longitudinal  pressure  on  the  magnetisation  of  cobalt  have  been 
examined  by  Mr.  C.  Chree,*  who  found  a  reversal  of  effect,  as 
the  magnetisation  was  increased,  resembling  the  Villari  reversal 
in  iron,  but  opposite  to  it  in  character.  In  iron,  as  we  have 
already  seen,  after  the  first  effects  of  stress  are  past,  pressure 
will  reduce  magnetism  in  weak  fields,  but  will  increase  it  in 
strong  fields.  In  cobalt  the  reverse  happens ;  pressure  increases 
magnetism  in  weak  fields,  but  reduces  magnetism  in  strong 
fields.  This  may  be  shown  either  by  magnetising  when  the 
pressure  is  on,  and  again  when  it  is  off,  or  by  applying  and 
removing  pressure  while  a  constant  magnetising  force  is  in 


^so° 

« 


^ 

&300 
1 200 


, 

/    / 


10         20        30         40          50     -.60         70        BO         90        100        110        120       130         14-0       iSt 

Magnetic    Force    H. 

FIG.  112. — Induced  and  Eesidual  Magnetisation  of  Cobalt  with  and  without 
Compressive  Stress. 

action.  If  the  latter  plan  is  followed,  we  have,  of  course,  to 
exclude  the  initial  effects,  which,  as  Mr.  Chree  has  pointed  out, 
occur  in  cobalt  as  they  occur  in  iron.  The  first  application  of 
pressure  in  weak  fields  causes  a  large  increase  of  induced  mag- 
netism, just  as,  we  may  anticipate,  the  first  application  or 
removal  of  stress  of  any  kind  would  do  ;  but  repetition  of  the 
process  soon  establishes  a  cyclic  state. 

The  effects  of  longitudinal  pressure  in  modifying  the  magneti- 
sation curve  of  cobalt  are  illustrated  in  Fig.  112  (from  an  ex- 
periment by  the  writer  and  Mr.  W.  Low).  The  full  lines  are  two 

*  Phil.  Trans.,  1890,  A,  p.  329  ;  Proc.  Koy.  Soc,,  December,  1889. 


224  MAGNETISM    IN    IRON. 

curves  of  induced  magnetism  for  a  rod  of  cast  cobalt,  tested 
(within  a  yoke)  without  stress,  and  also  with  a  compressiva 
stress  amounting  to  16 -2  kilogrammes  per  square  millimetre. 
The  broken  lines  are  the  corresponding  curves  of  residual 
magnetism.  The  induced  curves  cross,  illustrating  the  reversal 
described  by  Mr.  Chree.  The  residual  curves  do  not  cross 
within  the  limits  of  field  used  here ;  but  other  experiments, 
made  with  the  same  rod  but  with  heavier  loads,  show  a  crossing 
in  them  also.  Curves  of  the  permeability  in  terms  of  B,  drawn 
from  the  data  of  the  same  experiment,  have  already  been  given 
in  Fig.  42,  §  76. 

§132.  Relation  between  the  Effects  of  Stress  on  Mag- 
netism, and  the  Effects  of  Magnetism  in  Changing  the 
Dimensions  of  Magnetic  Metals. — In  his  book  on  "Applications 
of  Mathematics  to  Physics  and  Chemistry"  (p.  47  et  seq.),  Prof. 
J.  J.  Thomson  has  discussed  this  subject,  and  has  pointed  out 
that  it  is  possible,  from  theoretical  considerations,  to  predict  the 
general  character  of  the  effects  of  stress  from  a  knowledge  of 
the  changes  of  dimension  caused  by  magnetisation.  Mr.  Shelford 
Bid  well,  in  a  Paper  which  will  be  referred  to  later  in  more  detail,* 
has  shown  that  an  iron  rod  lengthens  when  it  is  magnetised,  pro- 
vided the  magnetising  force  does  not  exceed  a  certain  limit,  but 
shortens  if  the  force  does  exceed  that  limit.  Prof.  Thomson 
shows  that  this  reversal  of  effect  is  to  be  anticipated  from  the 
Villari  reversal  which  is  observed  in  the  effects  of  longitudinal 
stress.  Again,  a  nickel  rod  shortens  when  magnetised,  and  con- 
tinues to  shorten  under  high  magnetic  forces ;  this  agrees  with 
the  fact  that  in  nickel  there  is  no  Villari  reversal,  and  that 
longitudinal  pull  diminishes  the  magnetism,  whether  that  is 
weak  or  strong.  Again,  with  cobalt  Bidwell  has  found  effects 
opposite  to  those  found  in  iron,  namely,  that  weak  magnetisa- 
tion shortens  a  cobalt  rod  and  strong  magnetisation  lengthens 
it.  Applying  his  equations  to  this  result,  Prof.  Thomson 
has  anticipated  what  the  character  of  the  effects  of  stress  in 
cobalt  should  be.  Mr.  Chree's  experiments  have  verified  his 
conclusions,  by  showing  that  the  effects  of  stress  in  cobalt  are 
the  reverse  of  the  effects  of  stress  in  iron,  tension  diminishing 
weak  magnetism  but  augmenting  strong  magnetism,  f 

*  Phil.  Trans.,  1888,  A,  p.  205. 

t  See  the  introduction  to  Mr.  Chree's  Paper,  Phil.  Trans.,  1890,  A,  p.  329 


RESIDUAL   EFFECTS    OF   STRESS.  225 

§  133.  Residual  Effects  of  Stress  applied  before  Magnetis- 
ing.— Perhaps  the  most  interesting  of  all  the  effects  of  stress 
are  those  that  occur  in  unmagnetised  iron.  To  apply  and 
remove  load  before  beginning  to  magnetise  a  piece  of  iron  has 
been  found  to  affect  the  magnetic  susceptibility,  even  when  the 
load  is  well  within  the  elastic  limit,  and  when  the  piece  is  per- 
fectly free  from  magnetisation  during  application  and  removal 
of  the  load.  We  have,  in  fact,  evidence  that  even  in  unmag- 
netised iron  the  process  of  loading  and  unloading  causes  changes 
of  molecular  configuration  which  are  not  reversible.  These 
changes  exhibit  hysteresis  with  regard  to  the  loads  which  cause 
them.  They  affect  more  than  one  physical  quality  of  the  metal; 
in  particular,  they  produce  upon  the  magnetic  susceptibility 
an  effect  which  becomes  obvious  when  the  piece  is  magnetised. 
These  residual  effects  of  past  loads  may  be  wiped  out  by  sub- 
jecting the  piece  to  the  operation  of  demagnetising  by  reversals. 
They  may  also  be  wholly,  or  almost  wholly,  removed  by  tap- 
ping the  piece  smartly  and  so  causing  vibration. 

Hence,  in  experiments  designed  to  show  the  differences  of 
susceptibility  of  iron  or  steel  when  subjected  to  different 
amounts  of  load,  the  piece  should  be  passed  through  the  opera- 
tion of  demagnetising  by  reversals  after  the  load  has  been  put 
on.  This  procedure  was,  in  fact,  followed  in  the  experiments 
that  have  been  described  above. 

The  residual  effects  of  stress,  occurring  in  the  absence  of  any 
actual  magnetisation,  are  of  very  great  interest  in  their  bearing 
on  any  theory  of  the  molecular  constitution  of  magnetic  metals. 
One  or  two  experiments  by  the  present  writer  may  be  cited  to 
show  their  general  character.* 

Let  an  iron  wire  be  subjected  to  pulling  stress,  and  let  the 
load  be  removed  before  beginning  to  magnetise.  Then,  pro- 
vided the  load  which  has  been  applied  lies  within  the  elastic 
limit,  or  rs  less  than  some  load  by  which  the  wire  has  been 
previously  stretched,  we  observe  no  mechanical  change  of  any 
ordinary  kind  as  the  result  of  applying  and  removing  the  load. 
And  if,  before  beginning  to  take  a  curve  of  magnetisation,  we 
put  the  wire  through  the  process  of  demagnetising  by  reversals, 
we  shall  find  nothing  in  the  curve  to  show  whether  there  has  01 
has  not  been  any  application  of  load  before  that.  But  suppose, 
»  Phil.  Trans.,  1885,  Par)-  II.,  pp.  612-619. 


226  MAGNETISM    IN    IRON, 

after  the  process  of  demagnetising  has  been  gone  through,  we 
apply  and  remove  some  load  before  beginning  to  magnetise. 
Though  there  has  been  no  immediately  obvious  mechanical 
change,  the  wire  has  undergone  a  change  of  structure  which 
shows  itself  in  the  form  assumed  by  the  curve  of  magnetisation. 
We  find  the  magnetic  susceptibility,  especially  under  low  forces, 
much  greater  in  this  than  in  the  former  case.  The  whole  differ- 
ence in  procedure  may  be  no  more  than  this,  that  in  one  case  the 
load  is  removed  before  the  process  of  demagnetising  is  performed; 
in  the  other  case,  the  process  of  demagnetising  is  performed 
before  the  load  is  removed.  So  slight  a  difference  in  procedure 
might,  perhaps,  be  expected  to  have  no  influence  on  the  form  of 
the  curve  ;  in  fact,  however,  it  has  a  large  influence.  The  curve 
of  magnetisation  depends  not  merely  on  the  load  actually  pre- 
sent :  it  is  affected,  especially  in  its  early  portion,  by  any 
changes  of  load  which  have  taken  place  since  the  preceding 
demagnetisation.  For  instance,  it  has  been  observed  that  if  a 
curve  be  taken  with  (say)  a  pull  of  3  kilos  on  an  iron  wire, 
and  if,  after  complete  demagnetisation,  the  load  be  raised  to 
4  kilos  and  1  kilo  be  removed,  and  a  second  curve  be  then 
taken,  the  second  curve  will  differ  very  sensibly  from  the  first, 
in  spite  of  the  fact  that  the  wire  may  have  previously  been 
subjected  to  many  times  that  amount  of  load,  and  was,  there- 
fore, in  a  mechanically  stable  state. 

§  134.  Experiments  showing  Residual  Effects  of  Stress. — 
In  the  following  case  an  iron  wire*  (previously  hardened  by 
permanent  strain)  was  loaded  with  a  weight  of  18 '5  kilos,  or 
42 '5  kilos  per  sq.  mm.  This  weight  was  repeatedly  applied 
and  removed,  then  finally  removed ;  the  wire  was  demagnetised 
by  reversals,  and  the  magnetising  process  was  then  gone 
through,  giving  the  magnetometer  readings  stated  in  column  I. 
of  Table  XXIII.  Then  the  wire  was  demagnetised :  the  weight 
of  18*5  kilos  was  applied  and  removed,  and  then  the  process 
of  magnetising  was  again  gone  through,  giving  the  magneto- 
meter readings  in  column  II.  Finally,  the  same  thing  was  re- 
peated, but  with  this  difference,  that  the  wire  was  briskly 
tapped  after  the  load  had  been  removed  before  beginning  to 
magnetise ;  the  results  of  this  are  given  in  column  III. 

*  Loc.  cit.,  p.  614, 


HYSTERESIS   IN   MOLECULAR   DISPLACEMENTS. 


227 


TABLE  XXIII. — Magnetisation  of  Iron  under  the  influence  of 
previous  loads. 


Magnetometer  readings. 

H 

I. 

II. 

III. 

After 
demagnetisation 
with  no  load. 

After  the  cycle 
0-18^-0. 

After  the  cycle 
0-18J-0 

and  then  vibration. 

0 

0 

0 

0 

1-15 

5 

8 

5 

2-01 

11 

19 

10 

2-87 

19 

40 

17 

4-31 

44 

73 

35 

575 

78-5 

110 

70 

8-62 

149 

176 

150 

11-50 

212-5 

230 

214 

14-37 

267 

278 

268 

17-25 

314-5 

321 

314 

20-12 

355 

358-5 

354 

23-00 

390 

394 

388 

25-87 

420 

420 

422 

33-12 

472 

472 

471 

Comparing  the  three  columns,  it  will  be  clear  that  in  the 
first  and  third  case  the  metal  is  in  substantially  the  same  con- 
dition as  to  susceptibility.  In  the  third  case  its  susceptibility 
with  respect  to  low  magnetic  forces,  and  even  to  moderately 
great  forces,  has  been  notably  raised,  as  a  consequence  of  the 
molecular  change  brought  about  through  application  and  re- 
moval of  the  load.  The  same  change  had  occurred  in  the  other 
two  cases,  but  it  had  been  undone  by  the  demagnetising  pro- 
cess in  one,  by  vibration  in  the  other. 

Experiments  of  this  kind  lead  to  the  conclusion  that  when 
we  apply  and  remove  stress  in  iron,  even  when  the  magnetic 
state  is  perfectly  neutral,  we  cause  some  kind  of  molecular 
displacement  in  the  relation  of  which  to  the  applied  stress 
there  is  hysteresis.  When  any  load  is  applied  and  removed 
the  changes  of  molecular  configuration  lag  behind  the  changes 
of  stress.  We  accordingly  find,  if  we  stop  at  any  intermediate 
value  of  the  load  and  examine  the  susceptibility,  that  the 
result  is  not  the  same  when  the  stoppage  is  made  during  the 
process  of  loading,  as  when  it  is  made,  at  the  same  amount  of 


228 


MAGNETISM    IN    IRON. 


load,  during  the  process  of  unloading.  Magnetic  susceptibility 
may,  of  course,  be  thought  of  as  a  physical  property  of 
the  meta],  apart  from  the  existence  of  any  actual  magnetisa- 
tion. During  the  loading  and  unloading  of  an  unmagnetised 
piece  the  susceptibility  changes  in  a  manner  that  involves 
hysteresis,  just  as  the  magnetism  changes  when  we  load  and 
unload  a  magnetised  piece. 

TABLE    XXIV. — Magnetisation  of  Iron  under  the   influence  of 
previous  loads. 


Magnetometer  readings. 

I. 

ii. 

III. 

IV. 

Galvanometer 
readings. 
(To  reduce  to 
H  multiply  by 
0-0575.) 

Demagnetised 
with  no  load. 
ThenO-lS£-3. 
Load  =3  kilos. 

Demagnetised 
with  no  load. 
Then 
0-18fc-0-3. 
Load  =  3  kilos. 

Demagnetised 
with  no  load. 
Loaded  to  18J, 
unloaded  to  3 
kilos,  and 
tapped  before 
magnetising. 
Load  =3  kilos. 

Demagnetised 
with  no  load. 
Loaded  to  3  kilos 
and  tapped 
before  magnet- 
ising. 
Load  =  3  kilos. 

0 

0 

0 

0 

0 

25 

22 

13 

11 

10 

50 

70 

14 

36 

34 

75 

139 

109 

103 

100 

100 

198 

176 

174 

168 

125 

242 

226 

227 

219 

150 

276 

265 

268 

259 

200 

328 

323 

328 

320 

250 

365 

369 

365 

300 

398 

398 

403 

400 

350 

424 

425 

429 

427 

450 

461 

462 

467 

466 

588 

491 

494 

499 

498 

0 

274 

275 

277 

276 

In  Table  XXIV.  four  magnetisations  of  the  same  iron  wire 
are  exhibited,  each  under  a  pulling  load  of  3  kilos.*  In  I.,  the 
load  had  been  previously  raised  to  18  J  kilos,  then  reduced  to 
3  kilos.  In  II.,  the  condition  of  load  had  been  reached  by  ap- 
plying 3  kilos,  after  there  had  been  no  load.  In  III.  and  IV. 
these  differences  of  procedure  were  repeated,  but  the  wire  was 
subjected  to  vibration  before  the  magnetising  process  began. 
It  will  be  seen  that  between  I.  and  II.  there  is  a  marked  differ- 

*  Owe  kilo  of  load  here  corresponds  to  a  stress  of  2'3  kilos  per  sq.  mr»- 


EXAMPLES   OF   RESIDUAL   EFFECTS. 


229 


ence,  especially  in  the  early  portion  of  the  curve ;  but  in  III. 
and  IV.  this  difference  has  practically  disappeared,  the  effects 
of  hysteresis  being  destroyed  by  vibration. 

Again,  Fig.  113  shows  two  pairs  of  curves,  two  (I.  and  II.) 
taken  under  no  load,  and  two  (III.  and  IV.)  taken  under  a  load 
of  3  kilos.  In  I.,  the  wire  was  demagnetised  immediately  before 
the  curve  was  taken.  In  II.  it  was  demagnetised,  then  loaded 
with  15  kilos,  and  then  completely  unloaded.  In  III.  it  was 
loaded  with  10  kilos,  and  unloaded  down  to  3  kilos.  In  IV.  it 
was  completely  unloaded  from  10  kilos,  then  reloaded  up  to 
3  kilos.  Very  similar  differences  in  effect  have  been  observed 


\s- 


Magnetising    Force. 

FIG.  113. — Residual  Effects  of  Previous  Loads. 

when  annealed  iron  (not  previously  hardened  by  stretching) 
has  been  tested  under  corresponding  varieties  of  condition  in 
regard  to  previous  stress.* 

The  changes  in  molecular  structure  which,  as  these  results 
show,  are  going  on  in  iron  or  steel  during  the  process  of  ap- 
plying and  removing  stress  sometimes  result  in  producing  a 
small  amount  of  magnetism  in  a  piece  which,  after  being  mag 
netised,  has  been  brought  into  an  apparently  non-magnetic  state 
by  the  application  of  a  reversed  force.  There  are,  in  such  a 
case,  superposed  magnetisations  which  originally  neutralise  each 

*  Loc.  cit.,  p.  618. 


230  MAGNETISM    IN    IRON. 

other  so  far  as  external  effect  is  concerned,  but  the  balance  ia 
disturbed  through  the  unequal  action  of  the  stress  upon  them. 

§  135.  Other  Evidences  of  Hysteresis  in  the  Effects  of 
Stress. — These  experiments  show  that  the  structure  of  iron 
changes,  under  variation  of  stress,  in  a  manner  that  exhibits 
hysteresis,  that  is  to  say,  the  changes  of  structure  lag  behind 
the  changes  of  stress.  We  may  therefore  anticipate  that  we 
shall  find  traces  of  hysteresis  in  other  physical  qualities  besides 
magnetic  susceptibility  when  we  examine  the  variation  of  those 
qualities  under  variations  of  stress. 

A  remarkable  instance  is  furnished  by  the  thermo- electric 
quality  of  iron.  Under  variations  of  pull  the  thermo-electric 
quality  of  iron  varies  in  a  manner  which  strikingly  resembles 
those  variations  of  magnetic  quality  which  have  been  described 
in  this  chapter.  This  is  not  a  secondary  effect,  resulting  from 
changes  of  magnetism,  for  it  occurs  even  when  care  is  taken  to 
keep  the  iron  wholly  free  from  magnetisation  during  the  experi- 
ment. Curves  drawn  to  represent  the  relation  of  thermo-electric 
quality  to  load  show  a  very  remarkable  general  resemblance  to 
the  curves  of  Figs.  108-110,  which  show  the  relation  of  magnet- 
ism to  load.  There  are  also  interesting  points  of  difference, 
but  a  discussion  of  these  would  be  out  of  place  here.  The 
main  point,  which  was  discovered  by  E.  Cohn*,  and  afterwards, 
independently,  by  the  writerf,  is  that  there  is  much  hysteresis 
of  thermo-electric  quality  with  respect  to  stress — a  result,  no 
doubt,  of  the  irreversible  changes  of  molecular  structure  to 
which  allusion  has  just  been  made.  We  shall  see  later,  in 
connection  with  molecular  theories  of  magnetism,  how  these 
irreversible  changes  probably  occur. 

Further,  but  slighter,  evidence  of  the  occurrence  of  irrever- 
sible molecular  changes  during  the  loading  and  unloading  of  an 
iron  wire  is  found  when  we  examine  the  amount  of  the  exten- 
sion in  relation  to  the  load.  Though  the  amount  of  load  be 
restricted  so  that  it  lies  well  within  the  so-called  limit  of  elasti- 
city, it  is  found  that  there  is  no  exact  proportionality  of  strain 
to  stress  ;  and  when  a  cyclic  process  of  loading  is  repeated  often 
enough  to  make  the  elongation  and  retraction  become  also 

*  Cohn,    Wied.  Ann.,  1879,  VI,  p.  385. 

t  Proc.  Roy.  Soc.,  1881,  XXXII.,  p.  399  ;  Phil.  Trans.,  1886,  p.  361. 


EFFECTS   OF   TORSION.  231 

cyclic,  it  is  found  that,  at  any  intermediate  value  of  the  load, 
the  wire  is  longer  during  unloading  than  during  loading.  In 
other  words,  there  is  hysteresis  in  the  relation  of  strain  to  stress. 
The  amount  of  this  hysteresis  is  small ;  but  when  means  are 
taken  to  magnify  the  extension  sufficiently  it  may  be  observed 
without  difficulty.  The  amount  of  difference  in  length  between 
the  length  at  the  mean  load  in  loading  and  the  length  at  the 
mean  load  in  unloading,  may  be  ^J^-  of  the  change  of  the  whole 
extension.  The  effect  in  question  has  to  be  distinguished  from 
quasi-plastic  changes  of  length,  which  depend  on  the  time-rate 
at  which  the  loads  are  applied.  It  has  been  observed  in  wires 
of  copper  and  brass,  as  well  as  iron  and  steel.*  One  obvious 
consequence  of  it  is  that  any  process  of  loading  and  unloading 
involves  some  dissipation  of  energy. 

§136.  Effects  of  Torsion  on  Magnetic  Quality.— The  k 
fluence  of  twisting  strain  on  the  magnetic  quality  of  metals 
has  engaged  the  attention  of  many  experimentalists,  beginning 
with  Matteucci,t  who,  in  1847,  examined  ballistically  the  change 
of  magnetism  undergone  by  an  iron  rod  when  it  was  twisted 
back  and  forth,  while  a  magnetising  current  was  kept  up  in  a 
surrounding  solenoid.  Wertheim,  E.  Becquerel,  and  Wiede- 
mann  followed  on  the  same  lines,  |  and  the  subject  was  taken 
up  by  Lord  Kelvin  in  one  of  the  sections  of  his  in- 
vestigation of  the  electro-dynamic  qualities  of  metals. ||  More 
recently  a  number  of  other  workers  have  pursued  the  matter 
in  great  detail.  The  results  of  their  investigations  are  much 
too  complicated  to  admit  of  anything  like  full  statement  here ; 
we  must  be  content  with  an  account  of  some  of  the  more 
conspicuous  facts. 

The  general  result  of  early  experiments  was  to  show  that  when 
a  rod  of  soft  iron,  exposed  to  longitudinal  magnetising  force, 
was  twisted,  its  magnetism  was  reduced,  by  torsion  in  either 
direction.  In  this  effect,  as  in  all  effects  of  stress,  we  have 
to  distinguish  between  the  irreversible  initial  effect  of  the 

*  Brit.  Assoc.  Rep.,  1889,  p.  502. 
t  Comptcs  Rendus,  Vol.  XXIV.,  p.  301. 

t  For  an  abstract  of  these   researches,  see  "VViedemann's  EleJctricitdt, 
Vol.  III.,  p.  671,  et  seq.  ;  see  also  "Wiedeinann,  Phil.  Mag.,  1886. 
U  Phil.  Trans.,  1878  j  Reprint  of  Papers,  Vol.  II.,  p.  374. 


232 


MAGNETISM    IN    IRON. 


first  application  (due  to  molecular  instability)  and  the 
effect  which  becomes  manifest  when  a  cycle  of  strain  is 
repeated.  The  initial  effect  of  torsion  will  depend  on  the  past 
history  of  the  piece,  but  the  cyclic  effect  is,  in  soft  iron,  of  this 
character,  that  twisting,  to  either  side,  reduces  the  induced 
magnetism,  and  untwisting  increases  it.  But  this  effect  is  very 
small  for  small  angles  of  twist.  Moreover,  as  with  other  effects 
of  stress,  the  changes  of  magnetism  exhibit  hysteresis.  This 
was  pointed  out  in  1878  by  Kelvin,  who  has  given  curves 
showing  the  manner  in  which  the  magnetism  induced  in  an 
iron  wire  by  a  constant  magnetic  field  changes  as  one  end  of 
the  iron  wire  is  twisted  to  and  fro  while  the  other  end  is  held 


*NGLE  OF  TWIST 

Fia.  114. — Effect  of  Twist  on  the  Magnetism  of  Iron. 

fixed.  The  typical  form  into  which  the  curves  settle  after 
repeated  twistings  is  shown  in  Fig.  114,  which  is  copied  from  his 
Paper.  From  the  form  of  these  curves  it  is  clear  that  if  the 
effects  of  hysteresis  were  eliminated — as  they  no  doubt  might 
be,  at  least  in  part,  by  vibrating  the  wire — we  should  have  a 
single  curve  resembling  a  parabola  with  its  vertex  at  the  top 
of  the  diagram.  Thus  in  the  absence  of  hysteresis  we  should 
find  the  influence  of  torsion  in  reducing  the  induced  magnetism 
to  be  indefinitely  small  for  small  angles  of  twist,  and  to  increase 
initially  in  proportion  to  the  square  of  the  twist. 

§  137.  Effects  of  Torsion  due  to  Magnetic  Aeolotropy.— 

Sir  William  Thomson   has,   in  fact,  pointed    out   that  these 


EFFECTS   OF   TORSION. 


233 


results  are  to  be  anticipated  from  what  is  known  regarding 
the  effects  of  simple  pulling  and  simple  compression  on  the 
magnetic  susceptibility  of  iron.*  Experiments  in  which 
the  metal  is  subjected  to  longitudinal  pull  or  push  and 
to  transverse  pull,  have  shown  that  a  simple  pulling  stress 
or  a  simple  pushing  stress  develops  an  seolotropic  quality  in 
respect  of  magnetic  susceptibility,  producing  (in  iron)  greater 
susceptibility  along  than  across  the  lines  of  pull,  or  less  sus- 
ceptibility along  than  across  the  lines  of  push,  provided  the 
magnetisation  be  not  so  strong  as  to  pass  the  Villari  critical 
value.  Now  in  torsional  strain,  each  portion  of  the  twisted  rod 
experiences  a  simple  shearing  stress,  which  may  be  regarded  as 
made  up  of  a  pulling  stress  in  a  direction  inclined  at  45deg.  to 


Fia.  115. 

the  direction  of  the  length,  and  an  equal  pushing  stress  also 
inclined  at  45deg.  and  at  right  angles  to  the  pulling  stress. 
Thus,  if  a  b  c  d  (Fig.  115)  is  a  particle  anywhere  in  the  front 
half  of  the  rod,  which  is  twisted  in  the  manner  shown  by  the 
arrows,  the  twisting  produces  a  shearing  stress  in  a  b  c  d  that 
is  equivalent  to  a  pull  on  the  faces  a  b  and  c  d,  combined  with 
an  equal  push  on  the  faces  d  a  and  b  c.  The  effect  is  to  in- 
crease the  magnetic  susceptibility  along  the  direction  p  p  and 
to  reduce  it  along  p'  p'.  For  small  stresses  these  effects  are 
no  doubt  equal.  Hence  in  the  direction  of  the  length  of  the 
*  Reprint  of  Papers,  Vol.  II.,  p.  374.  ' 


234  MAGNETISM   IN   IRON. 

rod,  which  is  equally  inclined  to  p  p  and  p  p,  there  is,  virtually, 
no  change  of  susceptibility. 

The  effect  of  torsion  is  to  give  a  helical  quality  to  the  magne- 
tisation, producing  a  circular  component  which  is  superposed 
upon  the  original  longitudinal  magnetisation.  The  lines  of 
magnetisation  are  no  longer  coincident  in  direction  with  the 
lines  of  magnetic  force;  they  become  in  the  case  considered 
above  right-handed  screws.  The  effect  of  this  on  the  magni- 
tude of  the  longitudinal  component  is  at  first  indefinitely  small, 
but  as  the  angle  of  torsion  increases  the  growth  of  the  circular 
component  begins  to  detract  from  the  longitudinal  magnetism, 
for  magnetisation  in  one  direction  is  prejudicial  to  magnetisation 
in  other  directions,  as  the  molecular  theory  and  the  phenomenon 
of  saturation  suggest. 

This  consideration  of  the  magnetic  aeolotropy  produced  by 
the  pull  and  push  into  which  torsional  stress  may  be  resolved 
supplies  a  key  to  many  of  the  observed  facts  about  magnetism 
and  torsion.  At  the  same  time  it  fails  to  explain  many  of  the 
facts.  The  influence  of  seolotropy  is,  no  doubt,  always  present 
in  the  phenomena  of  torsion,  but  other  considerations  of  a  less 
obvious  kind  also  enter,  and  these  become  in  some  instances  so 
influential  that  the  effects  of  seolotropy  are  entirely  masked. 
This  is  notably  the  case  with  nickel.  With  soft  iron,  on  the 
other  hand,  most  of  the  observed  effects  of  torsion  admit  of 
fairly  complete  explanation  in  the  lines  suggested  by  Lord 
Kelvin,  especially  when  allowance  is  made  for  the  complications 
to  be  anticipated  from  hysteresis. 

§  138.  Production  of  Longitudinal  Magnetism  by  Twisting 
a  Circularly  Magnetised  Wire. — From  the  foregoing  account 
of  how  a  circular  component  of  magnetisation  is  developed  by 
torsion  in  a  longitudinally  magnetised  wire  or  rod,  it  will  be 
evident  that  the  converse  action  should  occur,  namely,  that 
twisting  a  circularly  magnetised  rod  should  make  it  develop 
longitudinal  magnetism.  This  fact  was  observed  in  1858  by 
Wiedemann,  who  found  that  an  iron  wire  conducting  an 
electric  current,  and  therefore  circularly  magnetised,  becomes 
a  magnet  when  twisted.*  Following  Kelvin,  we  may  ex- 

*  Elektricitat,  Vol.  III.,  p.  680. 


MAGNETISATION    DUE    TO    TWISTING. 


235 


plain  this  observation  as  a  consequence  of  seolotropy  by  re- 
solving the  magnetising  force,  whose  direction  is  0  A  (Fig.  116), 
into  components  along  the  lines  of  pull,  Op,  and  push,  Op'. 
Taking  the  case  of  iron,  below  the  Villari  critical  point,  and 
twisted  in  the  manner  shown  in  the  diagram,  the  susceptibility 
is  greater  along  the  lines  of  pull,  0  p,  than  along  the  lines  of 
push,  0  p'.  Hence  the  resultant  magnetisation  will  be  less 
inclined  to  Op  than  to  Op' ;  in  other  words,  it  will  take 
some  direction,  0  R,  which  gives  a  longitudinal  component  of 
magnetisation  directed  towards  the  bottom  of  the  rod.  This 
is,  in  fact,  the  kind  of  longitudinal  magnetism  which  is 
found. 


FIG.  116. 


It  might,  however,  be  supposed,  in  view  of  the  Villari  re- 
versal, that  under  sufficiently  strong  circular  magnetisation  the 
longitudinal  component  developed  by  twisting  would  become 
reversed.  Experiment  shows  that  this  does  not  happen  even 
when  a  very  strong  current  traverses  the  wire.  The  explana- 
tion appears  to  lie  in  the  fact  that  the  stresses  of  pull  or 
push  due  to  torsion  act  not  on  the  whole  intensity  of  circular 
magnetisation  but  on  components  inclined  at  45deg.  Hence, 
though  the  circular  magnetising  force  be  strong  enough  to 
bring  about  saturation,  the  components  of  magnetisation  on 
which  the  pull  and  push  act  remain  below  the  Villari  critical 


236  MAGNETISM   IN   IRON. 

value,  so  that  the  effect  of  pull  is  still  to  augment  and  of 
push  to  diminish  the  components  on  which  the  pull  and 
push  act.* 

These  effects  of  torsion  are  found  in  dealing  with  residual 
magnetism  as  well  as  with  induced.  In  Wiedemann's  experi- 
ment the  same  result  (namely,  the  production  of  longitudinal 
magnetism  by  torsion)  is  noticed  though  the  wire  be  not  twisted 
until  the  current  has  ceased  to  pass.  There  is  then  a  strong 
residual  circular  magnetism  which  is  affected  by  torsion,  just 
as  might  be  anticipated  from  the  fact  that  the  residual  mag- 
netism of  a  bar  magnetised  in  the  usual  way  is  affected  like 
induced  magnetism  by  pull  and  push. 

§  139.  Torsional  Strain  produced  by  Combining  Circular 
with  Longitudinal  Magnetisation. — A  similar  explanation 
applies  to  another  discovery  of  Wiedemann's,  namely,  that  if  an 
iron  wire  or  rod  be  both  circularly  and  longitudinally  magne- 
tised, it  becomes  twisted,  though  no  external  mechanical  force 
be  used.  The  superposition  of  the  two  magnetisms  turns  the 
lines  of  magnetisation  into  screws,  and  the  consequent  expan- 
sion along  the  lines  of  the  screws  and  contraction  across  these 
lines  causes  the  rod  to  twist.  In  iron  the  effect  of  mag- 
netising (unless  the  magnetising  force  be  very  strong)  is  to 
lengthen  the  metal  in  the  direction  of  magnetisation.  The 
direction  which  the  twist  is  observed  to  take  agrees  with 
this. 

In  nickel,  on  the  other  hand,  the  effect  of  magnetising  is  to 
shorten  the  metal  in  the  direction  of  the  lines  of  force.  The 
twist  taken  by  a  nickel  wire,  subjected  to  superposed  longitu- 
dinal and  circular  magnetising  forces,  is  accordingly  opposite  to 
that  of  iron,  as  Prof.  Knott  has  shownf  by  making  a  current 
traverse  a  nickel  wire,  which  was  at  the  same  time  exposed  to 
the  action  of  a  magnetising  solenoid. 

*  This  absence  of  reversal  is  referred  to  in  Kelvin's  Paper  as  a 
difficulty  ;  but  the  difficulty  disappears  when  it  is  recognised  that  the 
Villari  reversal  depends  rather  on  the  value  I  in  the  direction  of  pull  and 
push  than  on  the  value  of  H.  Though  the  components  of  H  along  direc- 
tions inclined  at  45deg.  to  the  axis  may  be  indefinitely  increased  by  in- 
creasing the  whole  magnetising  force,  the  components  of  I  along  these  lines 
remain  too  small  to  allow  pull  to  produce  reduction  of  magnetism. 

t  Trans.  Roy.  Soc.  Edin.,  Vol.  XXXII.  (1883),  p.  193. 


TRANSIENT    CURRENTS   DUE    TO    TWISTING. 


237 


§  140.  Transient  Currents  produced  by  Magnetising 
Twisted  Rods,  or  by  Twisting  Magnetised  Rods. — The  sud- 
den development  of  circular  magnetism  when  a  longitudinally 
magnetised  rod  is  suddenly  twisted,  or  when  a  longitudinal 
magnetising  force  is  suddenly  applied  to  a  rod  that  is  held  in  a  - 
state  of  torsion,  is  well  shown  by  connecting  the  ends  of  the; 
rods  to  a  galvanometer,  when  it  will  be  found  that  a  transient; 
current  is  induced  along  the  rod.  A  still  more  effective  ex-! 
periment  may  be  arranged  by  substituting  a  tube  for  the  solid 
rod,  and  by  placing  within  it  an  insulated  wire  in  circuit  with 


10  i 


\/eo 


OF  'fwiST 


-30 


-40 


60 


FIQ.  117.— Circular  Magnetisation  produced  by  Twisting  Magnetised  Iron. 

the  galvanometer.*  In  experiments  of  this  class  the  existence 
of  hysteresis  is  shown  in  an  interesting  way  by  making  back 
and  forth  twisting  take  place  in  a  series  of  steps,  when,  by 
summing  the  transient  currents,  it  is  at  once  seen  that  the 
circular  magnetisation  exhibits  hysteresis  with  respect  to  the 
angle  of  twist — a  result  which  is  of  course  to  be  anticipated 
from  the  known  effects  of  pull  and  push.  Thus  in  Fig.  117  an 
iron  wire  rather  strongly  magnetised  in  the  direction  of  its 
length  was  twisted  alternately  to  opposite  sides,  but  the  twist- 
*  Ewing,  Proc.  Roy.  Soc,  1883,  p.  117  ;  1881,  p.  21. 


238 


MAGXETISM    IN    IRON. 


ing  was  done  in  a  series  of  steps,  and  the  transient  current  for 
each  step  was  noted. 

Summing  up  the  transient  currents  we  obtain  the  circular 
magnetisation  in  arbitrary  units.  The  full  lines  of  the  figure 
show  how  the  circular  magnetisation  was  cyclically  reversed  by 
reversing  the  twist,  but  the  change  of  circular  magnetism  lagged 
behind  the  change  of  twist.*  The  dotted  line  in  the  same  figure 
exhibits  the  amount  of  circular  magnetism  found  by  first 
applying  a  given  torsion  and  then  reversing  the  longitudinal 


25 

/ 

/' 

g 

|^7 

'      •  •*, 

/ 

*r      : 

If 

X, 

/ 

/I 

f 

NGLEC 

2; 

FTWIS 

r    / 

f 

/ 

7  J 

/ 

O           3 
*         / 

oy    e 

0°         9 

7 

\^^ 

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V 

1  — 

:—  -  <TO 

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s' 

-25 

Fia.  118.— Circular  Magnetisation  produced  by  Twisting  Magnetised  Steel. 

magnetising  force.  This  procedure,  of  course,  eliminates  the 
hysteresis  which  appears  in  the  other. 

Fig.  118  gives  the  results  of  a  similar  experiment  made  with 
a  piece  of  pianoforte  steel  wire  in  its  usual  condition  of  temper. 
The  dotted  line  has  the  same  meaning  as  in  Fig.  117. 

In  these  cases  the  process  of  back  and  forth  twisting  had 

*  It  was  in  connection  with  this  instance  of  lagging,  one  of  the  first 
which  the  author  met  with  in  his  experiments,  that  the  word  "  hysteresis  " 
was  originally  introduced.  (Proc.  Roy.  Soc.,  1881,  p.  22.) 


ESTABLISHMENT    OF    CYCLIC    STATE. 


239 


been  repeated  often  enough  to  bring  about  a  cyclic  regime 
before  the  observations  were  taken.     It  is  interesting  to  notice 
the  manner  in  which  the  cyclic  state  is  reached.    This  is  shown 
in  Fig.  119,  which  relates  to  the  same  wire  as  Fig.  118.    Start- 
ing from  the  condition  that  had  been  reached  by  reversing  the; 
longitudinal   magnetisation,    when    the    angle   of    twist    was" 
+  90deg.,  the  changes  shown  in  the  diagram   were   brought 
about  by  twisting  back  to  —  90deg.,  again  to  +  90deg.,  back  to 
-  90deg.,  and  again  to  4-  90deg. 
In  all  these  cases  the  direction  of  the  circular  magnetisation 


Fra.  119.— Effects  of  Twist. 


was  such'  as  would  correspond  to  increase  of  magnetism  by  pull. 
The  current  flows  from  the  North  to  the  South  pole  when  the 
wire  or  tube  is  twisted  like  a  common  or  right-handed  screw. 
And  a  careful  inquiry  has  shown  that  the  effect  of  torsion  is 
always  of  this  character  in  iron :  that  is  to  say,  the  effect  is  not 
reversed,  though  the  longitudinal  magnetising  force  be  made 
very  great.  What  happens  in  that  event  is  that  the  transient 
currents  due  to  torsion  become  exceedingly  small ;  but  their 
sign  does  not  change.  Here,  again,  the  explanation  is  that 
the  intensity  of  magnetism  on  which  the  pull  and  push  of 


240  MAGNETISM    IN   IRON. 

the  torsion  act,  is  the  component  at  45  degrees  to  the 
axis,  and  this  remains  below  the  Villari  critical  value,  even 
when  the  whole  magnetism  approaches  saturation*  (see  §  138, 
ante). 

When  this  longitudinal  magnetism  is  residual  instead  of  in- 
duced, torsion  still  produces  transient  currents  of  the  same 
general  character,  but  the  effects  are  complicated  by  a  pro- 
gressive shaking  out  of  the  magnetism,  f 

Using  a  telephone  in  place  of  a  ballistic  galvanometer,  Hughes 
has  observed  the  production  of  transient  currents  in  a  twisted 
wire,  when  the  current  in  a  surrounding  solenoid  is  rapidly 
interrupted  or  reversed.  He  has  also  illustrated  the  produc- 
tion of  longitudinal  out  of  circular  magnetism  in  a  twisted 
wire,  by  passing  an  interrupted  current  through  the  wire,  and 
putting  a  telephone  in  circuit  with  a  coil  wound  round  the 
wire.  J 

In  nickel,  the  effects  of  simple  pull  and  push  are,  as  we  have 
seen,  opposite  in  sign  to  the  effects  in  iron,  provided  the  magneti- 
sation of  the  iron  is  not  so  great  as  to  cause  the  Villari  reversal. 
Hence  we  may  expect  the  transient  currents  produced  by  twist- 
ing a  longitudinally  magnetised  nickel  rod  or  tube  to  take  the 
opposite  direction  to  that  which  they  take  in  iron.  This  fact  has 
been  verified  by  the  independent  experiments  of  Zehnder  §  and 
Nagaoka,||  who  found  that  when  a  nickel  wire  is  twisted  as  a 
right-handed  screw  the  transient  current  flows  from  the  south 
to  the  north  pole. 

§  141.  Effects  of  Combined  Pull  and  Torsion  on  the  Mag- 
netisation of  Iron  and  Nickel. — The  same  observers  have 
recently  examined,  in  much  detail,  the  changes  of  magnetism 
in  iron  and  nickel,  which  occur  when  a  rod  is  subjected  at  the 
same  time  to  pull  and  twist,  and  Nagaoka  has  also  determined 
the  curves  of  magnetisation  which  are  given  by  nickel  wires 
when  kept  in  this  complicated  condition  of  stress.  Many  of  the 

*  Proc.  Roy.  Soc.,  1883,  p.  129. 
t  Loc.  cit.,  p.  126. 
£  Proc.  Roy.  Soc.,  Vol.  XXXI. 
§  Wied.  Ann.,  1889,  Vol.  XXXVIII. ,  p.  68. 

||  Jour.  Coll.  of  Science,  Imperial  Univ.  of  Japan,  Vol.  III.,  1890, 
p.  335. 


EFFECTS    OF    TWIST    IN    NICKEL.  24:1 

results  are  of  great  interest,  and  space  must  be  found  for  a  brief 
notice  of  some  of  them  here.* 

In  the  magnetisation  of  any  of  the  magnetic  metals  we  may 
distinguish  broadly  between  three  successive  stages  in  the  pro- 
cess. There  is,  first,  the  early  stage,  during  which  the  suscepti- 
bility is  comparatively  small:  the  curve  of  magnetisation  shows 
at  the  beginning  a  comparatively  easy  gradient.  Then  there  is 
the  middle  stage,  a  stage  of  high  susceptibility,  when  the  curve 
has  bent  upwards  and  rises  rapidly  towards  the  "wendepunct." 
Lastly,  there  is  the  third  stage,  in  which  the  condition  of  the 
specimen  may  be  spoken  of,  rather  loosely,  as  nearly  saturated. 
In  the  third  stage  the  curve  has  passed  the  "wendepunct,"  and 
has  again  taken  an  easy  gradient :  the  susceptibility  rapidly 
diminishes. 

In  specimens  which  are  free  from  stress  during  the  process 
of  magnetisation  these  three  stages  are  to  some  extent  blended, 
but  are  still  fairly  distinguishable,  as  a  reference  to  any  of  the 
figures  which  have  been  given  for  iron,  steel,  nickel,  or  cobalt 
will  show.  By  applying  torsion,  and  still  more  by  applying 
both  torsion  and  longitudinal  pull,  it  is  possible  to  differentiate 
the  stages  to  a  very  remarkable  degree.  This  is  shown  by 
Nagaoka's  experiments  on  nickel  wires,  which  are  illustrated  in 
the  following  figures.! 

Fig.  120  shows  the  influence  of  simple  torsion.  The  curve 
a  a  is  the  ordinary  magnetisation  curve  of  a  long  nickel  wire, 
annealed  and  tested  (without  torsion)  by  applying  and  removing 
a  magnetising  force  of  about  30  C.-G.-S.  units.  The  curve  b  b 
was  taken  while  the  wire  was  held  twisted,  the  amount  of  the 
twist  being  3°  per  centimetre  of  length. 

As  the  diameter  of  the  wire  was  1  millimetre,  this  amount  of 

twist  corresponds  to  an  angle  of  shear  of ^^: or  0'0026 

loU 

radians  at  the   circumference,   where  the   shearing   strain   is 
greatest. 

*  See  Papers  by  Nagaoka,  Jour.  Coll.  Science,  Imp.  Univ.  Japan,  Vol.  II., 
1888,  p.  283,  p.  304  ;  Vol.  III.,  1889,  p.  189 ;  Zehnder,  Wied.  Ann.,  1890, 
Vol.  XLL,  p.  210  ;  also  Papers  by  Prof.  Knott,  Jour.  Coll.  Science,  Imp. 
Univ.  Japan,  Vol.  III.,  1889,  p.  173  ;  Proc.  R.  S.  E.,  Vol.  XVII.,  1890, 
p.  401,  and  Vol.  XVIII.,  1891,  p.  124. 

t  Jour.  Coll.  Science,  Imp.  Univ.  Japan,  Vol.  II.,  p.  304. 

B 


242 


MAGNETISM    IN    IRON. 


The  curve  taken  when  the  wire  was  under  torsion  exhibits 
some  striking  differences  from  the  other.  In  the  first  place, 
the  initial  susceptibility  (with  respect  to  feeble  magnetic  forces) 
is  greatly  lowered  by  torsion.  The  first  part  of  the  magnetising 
process  is  sharply  distinguished  from  the  second  stage.  When 
the  second  stage  is  reached,  the  twisted  wire  has  very  great 


350 


300 


250 


200 


100 


50 


0 


25 


30 


5  10  15  20 

Magnetic  Force  H 

Fio.  120.— Magnetisation  of  Nickel:  a  a,  without  torsion  ;  6  J,  with  torsion. 

differential  susceptibility.  Again,  the  "  wendepunct "  in  it  is  com- 
paratively sharp.  Finally,  by  comparing  the  curves  got  during 
the  removal  of  magnetising  force,  we  see  that  the  twisted  wire 
possesses  much  more  retentiveness  than  the  other ;  the  ratio  of 
residual  to  induced  magnetism  in  it  has  the  remarkably  high 
value  of  0'97,  whereas  in  the  untwisted  wire  the  ratio  of  these 


EFFECTS    OF   PULL   AND    TWIST    IN    NICKEL. 


243 


quantities  is  only  075.  If  the  comparison  of  residual  mag- 
netisms were  made  at  earlier  points  in  the  magnetising  pro- 
cess, this  difference  would  be  still  more  marked. 

Mr.  Nagaoka's  experiments  further  prove  that  when  the 
angle  of  twist  is  considerably  increased  the  curve  shows  a 
slight  tendency  to  revert  towards  the  normal  type  (for  un- 
twisted wire).  It  must,  however,  be  borne  in  mind  that  any 
large  amount  of  torsion  complicates  the  conditions  of  the  expe- 
riment by  making  the  strain  pass  the  limit  of  elasticity. 


150 


100 


50 


^ 


10  15  20 

Magnetic  Force  H 


25 


30 


Fia.  121. — Magnetisation  of  Nickel :  c  c}  with  longitudinal  pull  only  ;  d  d, 
with  longitudinal  pull  and  torsion. 


More  curious  still  are  the  results  of  combining  torsion  with 
longitudinal  pull.  The  application  of  pull,  by  itself,  has  (as 
was  shown  in  §  121)  the  effect  of  lowering  the  magnetisa- 
tion curve  of  nickel.  When  twist  is  superposed  upon  pull 
the  initial  part  of  the  curve  is  still  further  lowered,  but  at  a 
moderately  great  value  of  the  magnetising  force  a  sudden 
change  takes  place,  the  differential  susceptibility  becomes 
enormous  throughout  a  narrow  range  of  values  of  the  magnet- 
ising force;  then  comes  a  somewhat  sharp  " wendepunct,"  and 
the  second  stage  is  followed  by  a  third  in  which  there  is  a  slow 
approach  to  saturation.  Fig.  121  is  selected  from  Nagaoka's 

R2 


244  MAGNETISM    IN    IRON. 

curves  to  illustrate  these  effects.  The  wire,  which  was  the  same 
specimen  of  nickel  as  before,  was  loaded  with  10  kilos.,  and 
the  curve  c  c  was  taken  while  there  was  no  twist.  Here,  as 
the  results  of  §  121  lead  us  to  expect,  there  is  low  susceptibility 
throughout  and  exceedingly  little  retentiveness.  Next,  a  steady 
twist  of  3°  per  centimetre  was  given  to  the  loaded  wire.  The 
curve  of  magnetisation  was  then  found  to  take  the  extraordinary 
form  shown  in  d  d,  with  reduced  initial  susceptibility,  which  lasts 
through  a  wide  range  of  force, — followed  by  an  abrupt  rise  of 
magnetism  in  a  field  of  about  12  to  13  C.-G.-S.,  and  then  high 
retentiveness.  We  have  here  a  quite  exceptionally  sharp 
definition  of  the  three  stages  in  the  magnetising  process,  and 
a  singularly  striking  display  of  hysteresis.  The  curves  of 
Figs.  120  and  121,  relating,  as  they  do,  to  the  same  specimen, 
form  one  group;  they  are,  moreover,  drawn  to  the  same 
scale.  a  a  is  the  normal  curve,  showing  the  behaviour  of 
the  metal  when  there  is  neither  pull  nor  twist ;  b  b  shows 
the  effect  of  twist  alone ;  c  c  shows  the  effect  of  pull  alone ; 
finally,  d  d  shows  the  effect  of  combining  the  twist  of  6  b  with 
the  pull  of  cc.  It  is  interesting  to  notice  that  the  whole 
amount  of  magnetism  which  is  acquired  during  the  second  or 
abrupt  stage  in  d  d  is  only  about  half  the  amount  that  is 
acquired  during  the  corresponding  stage  in  b  b. 

The  effects  of  twist  which  these  curves  exhibit  do  not  seem 
capable  of  explanation  by  reference  to  the  development  of  mag- 
netic seolotropy  in  consequence  of  the  pull  and  push  components 
of  torsional  stress.  The  inadequacy  of  this  explanation  will  be 
even  more  apparent  in  the  experiments  with  which  the  next 
paragraph  deals. 

§  142.  Effects  of  Cyclic  Twisting  in  Nickel,  when  associated 
with  Longitudinal  Pull. — The  combination  of  torsion  and  pull 
has  been  found  by  Nagaoka  to  have  an  even  more  extraordinary 
effect  on  the  magnetisation  of  nickel  if  the  torsion  be  sub- 
jected to  cyclic  reversals,  while  the  pull  is  maintained  constant. 
Let  a  nickel  wire  be  exposed  to  any  moderately  weak  magnet- 
ising force  in  the  direction  of  its  length,  and  let  one  end  be 
twisted  to  and  fro  while  the  other  end  is  held  fixed.  So  long 
as  there  is  no  longitudinal  pull  the  effects  of  this  alternating 
torsion  are  comparatively  simple.  The  curve  connecting  mag- 


EFFECTS   OF    CYCLIC   TWIST   IN    NICKEL.  245 

netism  with  angle  of  twist  has  a  symmetrical,  or  nearly  sym- 
metrical, form,  recalling  that  found  in  iron  (Fig.  114),  but 
with  the  important  difference  that,  in  nickel,  the  magnetism 
increases  with  twist  instead  of  diminishing  as  it  does  in  iron. 
This  difference  is  intelligible  enough,  in  view  of  the  opposite 
effects  of  pull  in  nickel  and  in  iron. 

But  let  the  experiment  of  twisting  to  and  fro  be  repeated 
when  a  weight  is  hung  from  the  wire  to  produce  a  steady 
longitudinal  pull.  It  is  now  found  that  the  symmetry  of  effect 
is  gone.  The  magnetism  is  much  increased  by  twisting  the 
wire  to  the  side  towards  which  the  earliest  twist  is  directed. 
Twisting  to  the  other  side  does  not  increase  the  magnetism 
nearly  so  much.  And  if  the  amount  of  steady  pull  be  suffici- 
ently increased,  this  want  of  symmetry  becomes  more  pro- 
nounced, until  a  very  peculiar  result'  is  brought  about — that, 
whereas  twisting  towards  one  side  increases  the  magnetism, 
twisting  towards  the  other  side  decreases  the  magnetism,  and 
may  even  decrease  it  so  much  as  to  reverse  its  sign. 

This  description  will  become  more  intelligible  if  reference  is 
made  to  Figs.  122,  123,  and  124,  which  illustrate  one  of 
Nagaoka's  experiments.  The  specimen  was  a  nickel  wire 
1  mm.  in  diameter  and  40  cms.  long,  tested  in  the  annealed 
state.  A  surrounding  solenoid  allowed  a  magnetising  force 
to  be  applied,  which  was  kept  constant  with  the  value  2 '47 
throughout  the  experiment.  In  the  first  instance  (Fig.  122) 
there  was  sensibly  no  longitudinal  pull.  Repeated  twistinga 
from  +180°  to  - 180°  brought  about  a  cyclic  state  of  things 
which  is  represented  in  the  figure.  Here  the  general  effect  of 
torsion  is  that  twisting  to  either  side  augments  the  magnetism. 
Next,  a  steady  longitudinal  pull  was  applied,  amounting  to  1  '45 
kilogrammes  per  square  millimetre,  and  the  process  of  twisting 
to  and  fro  was  repeated.  The  result  was  to  establish  the  cycle 
of  Fig.  123,  in  which  the  loop  of  the  curve  on  the  side  of 
positive  twist  is  much  more  prominent  than  the  loop  on  the  side 
of  negative  twist.  The  term  positive,  as  used  here,  simply  dis- 
tinguishes the  direction  which  happened  to  be  given  to  the 
twist  in  the  first  instance.  The  question  of  which  direction 
of  torsion  augments  the  magnetism  most  depends  simply  on 
which  is  the  direction  the  wire  is  first  twisted  in.  Next,  the 
longitudinal  pull  was  increased  by  adding  more  steady  load,  and 


246 


MAGNETISM   IN    IRON. 


it  was  found  that  the  positive  loop  of  the  curve  lengthened, 
while  the  negative  loop  became  more  insignificant.  Finally, 
the  negative  loop  disappeared,  and  with  a  load  of  7 '82  kilo- 
grammes  per  sq.  mm.,  the  cyclic  process  took  the  form  shown 
in  Fig.  124,  where  we  see  the  extraordinary  phenomenon  of  a 
reversal  of  magnetic  polarity  occurring  with  every  reversal  of 
torsion al  strain,  notwithstanding  the  fact  that  the  force  H  of 
2-47  units  was  continuously  operative  in  one  fixed  direction. 


280 


260 


240 


220 


200 


180 


160 


-i 


A 


180°          120"          60°  0  60° 

Angle  of  Twist. 
Fio.  122. 


120° 


ISO- 


It  is  clear  that  these  effects  of  twist  are  not  consequences 
of  seolotropy  in  the  twisted  material  in  respect  of  magnetic 
susceptibility.  In  fact,  the  inducing  magnetic  force  plays  a  very 
subordinate  part  in  the  changes  of  magnetism  which  take 
place  when  the  wire  is  twisted  to  and  fro,  after  a  cyclic  regime 
is  established.  Its  function  is  to  set  up  a  magnetic  condition 
to  begin  with ;  then,  as  the  wire  is  twisted  back  and  forth,  there 
is  with  each  twist  a  profound  change  in  the  molecular  con- 


REVERSAL  OP  POLARITY. 


247 


figuration,  This  Is  the  direct  result  of  the  twist,  and  may,  as 
in  the  case  last  described,  go  so  far  as  to  produce  reversal  of 
magnetic  polarity. 


220 


200 


180 


160 


140 


120 


100 


180° 


120' 


60°  0*  60' 

Angle  of  Twist. 

FIQ.  123. 


120° 


180* 


When  the  magnetising  field  is  sufficiently  strengthened, 
this  reversal  of  polarity  does  not  occur.  The  inducing  force 
then  asserts  itself,  and  the  effects  of  twist  come  to  be  more 


248 


0°     183° 


Fia.  124. 


STRAIN   DUB   TO   MAGNETISATION.  249 

nearly  such  as  might  be  anticipated  from  the  consideration  of 
seolotropy.  Iron  does  not  reverse  its  polarity  under  the 
combined  influence  of  pull  and  twist. 

§  143.  Strain  caused  by  Magnetisation. — Closely  associated 
with  the  changes  of  magnetisation  that  are  caused  by  strain 
are  the  changes  of  form  which  a  piece  of  iron,  or  other  magnetic 
metal,  is  observed  to  undergo  when  it  is  magnetised,  or  when 
its  magnetism  is  changed.  The  fact  that  strain  alters  mag- 
netism involves  this  converse,  that  change  of  magnetism  is 
accompanied  by  strain."*  The  earliest  experiments  on  the 
subject  were  those  of  Joule, f  who  found  that  the  length  of  a 
soft  iron  rod  was  increased  by  the  application  of  magnetising 
force,  within  the  limits  of  force  to  which  his  experiments  ex- 
tended. The  extension  was  accompanied  by  lateral  contraction, 
with  the  result  that  the  volume  of  the  rod  did  not  sensibly 
change.  To  show  this,  the  experiment  was  made  of  mag- 
netising the  rod  within  a  tube  full  of  liquid,  which  was  closed, 
except  for  an  extended  portion  with  a  narrow  bore,  the  rise  or 
fall  of  the  liquid  in  which  would  have  indicated  any  change  of 
volume  on  the  part  of  the  iron.  Later  experiments  on  the  ex- 
tension of  rods  were  made  by  Mayer,  J  who  dealt  specially  with 
steel ;  and  by  Barrett,§  who  extended  the  inquiry  to  nickel 
and  cobalt,  finding  that  nickel  retracted  when  magnetised.  It 
is  unnecessary  for  our  purpose  to  refer  to  these  early  experi- 
ments in  detail,  for  in  recent  years  the  matter  has  been  ex- 
haustively examined  by  Shelford  Bidwell,  whose  results  have 
harmonised  much  that  was  apparently  contradictory  in  the 
statements  of  previous  investigators.  Dealing  with  rings  as  well 
as  rods  (to  secure  uniform  magnetisation  and  determinate 
magnetising  forces),  Bidwell  has  tested  iron,  steel,  nickel,  and 
cobalt  throughout  a  very  wide  range  of  magnetising  force,  and 
has  found  that  when  the  force  is  pushed  to  high  values  the 
character  of  the  action  becomes  greatly  changed.  He  has  also 

*  See  Prof.  J.  J.  Thomson's  "Applications  of  Dynamics  to  Physics  and 
Chemistry,"  Chap.  IV. 

t  Joule,  Phil.  Mag.,  1847,  Vol.  XXX.,  pp.  76,  225.  Reprint  of  Papers, 
p.  235.  For  later  experiments  on  changes  of  volume  produced  by 
magnetisation,  see  Papers  by  Prof.  Knott,  Trans.  B.  S.  E.,  Vols.  38  and  39. 

t  Mayer,  Phil.  Mag.,  Vol.  XLVI.,  p.  177. 

§  Barrett,  Nature,  1882,  Vol.  XXVI.,  p.  58a 


250 


MAGNETISM    IN   IRON. 


examined  the  modifying  influence  of  externally  imposed  tensile 
stress  on  the  change  of  length  caused  by  magnetisation.  The 
following  is  a  brief  summary  of  the  more  important  of  his 
results.* 

The  method  of  experiment  is  shown  diagrammatically  in 
Fig.  125,  where  S  is  the  ring  to  be  tested.  The  change  of  length 
along  the  lines  of  magnetisation  was  deduced  by  observing  the 
change  in  the  diameter  of  the  ring  which  occurred  when  the 
magnetising  current  was  applied.  The  ring  S  was  placed  between 


E 


FIG.  125. 


a  fixed  support  E,  and  a  long  lever  B,  pivoted  on  a  fixed  fulcrum  at 
A.  The  long  end  of  the  lever  at  C  tilted  a  small  mirror  M  hinged 
on  a  fixed  support  by  a  knife  edge  at  D.  The  deflection  of 
the  mirror  was  read  by  means  of  a  distant  scale,  the  sensibility 
of  the  arrangement  being  such  that  readings  could  be  taken  corre- 
sponding to  about  one  ten-millionth  of  the  length  of  the  specimen. 
The  ring  was  jacketed  with  wood  to  exclude,  as  far  as  possible, 
the  heating  effect  of  the  magnetising  coil,  and  with  the  same 
object  the  circuit  was  never  allowed  to  remain  closed  for  more 
than  a  fraction  of  a  second.  A  similar  arrangement  was 

*  Shelford  Bidwell,  Proc.  Roy.  Soc.,  1886,  Vol.  XL.  pp.  109  and  257; 
Phil.  Trans.,  1888,  p.  205 ;  Proc.  Roy.  Soc.,  1890,  VoL  XLVIL,  p.  469. 


EFFECTS    IN    ALTERING    LENGTH.  25  J 

used  for  tests  of  rods.  The  ring  or  rod  was  first  demag- 
netised by  reversals,  then  a  current  of  known  strength  was 
passed  for  a  moment  through  the  magnetising  coil  and  the 
deflection  was  noted,  the  dead-beat  character  of  the  apparatus 
allowing  this  to  be  done  almost  instantaneously.  Then  the 
specimen  was  again  demagnetised  and  another  current  was 
applied,  and  so  on.  In  some  of  the  experiments  magnetising 
forces  approaching  1,500  C.-G.-S.  units  were  employed.* 

Beginning  with  small  magnetising  forces,  Bidwell  found  his 
iron  rods  and  rings  elongate  when  magnetised,  by  amounts  which 
appear  to  increase  at  first  in  something  like  simple  proportion 
to  the  degree  of  magnetisation.  But  as  the  magnetising  force 
increases,  the  elongation  of  iron  passes  a  maximum,  becomes 
reduced,  and  vanishes  when  the  magnetising  force  is  about 
300  C.-G.-S.  With  higher  forces  still,  the  iron  retracts  instead 
of  elongating  when  the  magnetising  force  is  applied,  and  this 
retraction  appears  to  tend  to  a  finite  limit  as  the  force  is  further 
increased.  The  maximum  amount  of  elongation,  which  is  ob- 
served in  comparatively  moderate  fields  (say  about  100  C.-G.-S.), 
varies  in  different  specimens  ;  it  ranged  in  Bidwell's  experiments 
from  about  T^nj-^nnF  to  TUUrtW  °^  tne  length.  The  amount  of 
retraction  under  very  strong  force  may  be  as  much  as  T-rvhnrG 
of  the  length.  These  figures  refer  to  iron.  Steel  behaves  in 
much  the  same  way,  but  suffers  less  elongation  than  iron  under 
moderate  forces. 

In  nickel,  on  the  other  hand,  there  is  retraction  from  the 
first,  and  the  amount  apparently  tends  to  a  fixed  limit  as  the 
magnetising  force  is  raised  to  high  values. 

In  cobalt  the  action  is  less  simple.  Weak  magnetising 
forces  cause  sensibly  no  change  of  length.  Stronger  forces 
cause  retraction,  but  the  amount  of  that  passes  a  maximum,  and 
vanishes  with  further  increase  of  the  force,  after  which,  with 
stronger  force  still,  there  is  extension,  the  amount  of  which  was 
still  increasing  fast  in  the  strongest  field  to  which  the  experi- 
ments were  carried.  These  results  are  well  shown  by  Figs. 
126  and  127,  taken  from  Bidwell's  principal  Paper.  In  Fig.  126 
the  magnetic  force  ranges  up  to  800  units.  In  Fig.  127 
it  is  carried  to  nearly  twice  that  value.  The  specimens  of 
metal  tested  were  different  in  the  two  cases;  the  general 
""•  Phil.  Trans.,  loc.  tit.  p.  227. 


252 


MAGNETISM    IN    IRON. 


results,  however,  agree  well.  The  nickel  used  in  the  experi- 
ment of  Fig.  127  shows  more  retraction  than  the  other.  The 
amount  of  retraction  under  the  strongest  magnetic  force  is 
about  of  the  original  length. 


SS  25 

•S 

HO 

r 

I 


.275 

ts 


Col)  lit 


Ma<j 


netic 


Fora 


H 


Fio.  126. — Elongation  and  Retraction  of  Iron,  Nickel,  and  Cobalt  through 
Magnetisation  (Bidwell).  The  elongations  and  retractions  are  stated  in 
ten-millionths  of  the  length. 


C50 


Fio.  127. — Elongation  and  Retraction  of  Iron,  Nickel,  and  Cobalt  through 
strong  Magnetisation  (Bidwell).  The  elongations  and  retractions  are 
stated  in  ten-millionths  of  the  length. 


§  144.    Modification  of  the  Results  by  applying  Tensile 
Stress. — In  a  later  Paper,*  Bidwell  has  described  experiments 
made  with  rods  of  iron,  nickel,  and  cobalt,  in  which  the  change 
*  Proc.  Roy.  Soc.,  1890,  p.  469. 


UNIVERSITY 


INFLUENCE    OF   PULL   ON   MAGNETIC   STRAIN. 


253 


of  length  caused  by  magnetisation  was  made  to  take  place 
while  a  load  was  hanging  from  the  specimen.  The  results  for 
iron  are  shown  in  Fig.  128,  the  numbers  attached  to  the  curves 
being  the  values  of  the  externally  applied  stress  in  kilo- 
grammes per  square  cm.  The  effect  of  tension  in  iron  in  to 
lower  the  curve,  reducing  the  maximum  extension  which  mag- 
netisation causes,  and  finally  making  it  vanish.  Under  the 
greatest  loads  used  in  these  experiments,  the  iron  retracted 
from  the  first  as  the  magnetising  force  was  increased. 

In  nickel  the  effect  of  tensile  stress  is  to  raise  the  curve  in 
its  earlier  stages,  making  the  amount  of  retraction  caused  by 


.£40 

I 


3CO 


FIG.  128.— Changes  of  Length  caused  by  magnetising  Iron  under  various 
amounts  of  longitudinal  pull  (Bidwell).  The  elongations  and  retractions 
are  stated  in  ten-millionths  of  the  length. 


magnetisation  less  if  the  test  is  made  while  there  Is  pull  than 
if  it  is  made  while  there  is  no  pull.  This  applies  to  magnet- 
ising forces  of  moderate  strength.  But  in  stronger  fields  the 
magnetic  contraction  is  increased  by  the  presence  of  small 
amounts  of  pull,  and  decreased  by  the  presence  of  large 
amounts  of  pull. 

In  cobalt,  the  changes  of  length  which  the  metal  undergoes 
in  being  magnetised  were  found  to  be  almost,  if  not  quite, 
independent  of  the  presence  of  pulling  stress.  Cobalt  stands 
in  striking  contrast  in  this  respect  to  iron  and  nickel,  in  both 
of  which  the  modifying  influence  of  pull  is  conspicuous. 


254  MAGNETISM    IN    IRON. 

§  145.  Stress  due  to  Magnetisation. — Attempts  have  been 
made  to  explain  some  part  of  the  retraction  which  is  observed 
in  experiments  such  as  these  to  the  state  of  internal  stress 
into  which  the  metal  is  thrown  by  its  magnetisation.  Imagine 
a  cross-section  to  be  taken  through  the  substance  of  a 
uniformly  magnetised  ring,  the  intensity  of  magnetism  in 
which  is  I.  The  surfaces  which  are  opposed  to  each  other 
at  the  plane  of  section  act  as  a  pair  of  plates  of  attracting 
matter,  the  surface  density  of  which  is  I.  The  force  which 
each  plate  exerts  on  unit  quantity  of  the  other  is  (by  a  well- 
known  proposition  in  the  theory  of  attraction)  2  ir  I.  But 
there  are  I  units  of  attracting  matter  per  unit  of  area  of  the 
plate:  hence  the  whole  force  exerted  by  one  plate  on  the  other 
is  2  TT  |a.  Thus,  if  the  ring  were  actually  cut  into  halves,  and 
the  half-rings  were  allowed  to  abut  against  each  other,  with 
say  a  slip  of  paper  between  the  iron  surfaces  at  each  joint, 
the  slip  of  paper  would  be  compressed  in  consequence  of  the 
magnetic  attraction  between  the  half-rings,  and  the  com- 
pressive  stress  acting  upon  it  would  be  equal  to  2  TT  I2  in  dynes 
per  square  centimetre.  Accordingly,  it  has  been  suggested 
that  in  an  uncut  magnetised  ring  there  is  a  circumferential 
stress  of  compression,  tending  to  shorten  the  metal  in  the 
direction  of  magnetisation.  It  may  readily  be  shown  that  such 
a  stress,  if  it  existed,  would  be  insufficient  to  explain  the 
retraction  which  iron  undergoes  when  it  is  magnetised.  But  it 
is  fallacious  to  conclude  that  any  such  stress  exists  in  the 
substance  of  the  uncut  ring.  There  is  no  proper  comparison 
between  the  state  of  stress  in  the  continuous-magnetised  ring 
and  the  state  of  stress  in  a  pillar  carrying  a  load.  We  may,  if 
we  please,  regard  the  magnetic  molecules  as  pulling  at  one 
another  across  any  imaginary  interface,  while  the  stress  with 
which  they  pull  is  balanced  by  thrust  in  the  framework  of  the 
iron,  but  neither  the  pull  nor  the  thrust  is  competent  to 
explain  the  mechanical  strains.* 

§  146.  Tractive  Force  in  Divided  Magnets. — The  remarks 
which  have  been  made  in  the  preceding  paragraphs  may  fitly  be 

*  See  a  correspondence  in  Natwe,  Vol.  LIIL,  1896,  pp.  269,  316,  317 
365,  462,  533  ;  and  Papers  by  Dr.  E.  Taylor  Jones,  Phil.  Mag.,  1896 ; 
Phil.  Trans.,  1897. 


MAGNETIC    TRACTION. 


255 


followed  up  by  a  reference  to  the  attraction  which  subsists 
between  two  portions  of  a  magnet  when,  instead  of  an  imaginary 
plane  of  section,  there  is  an  actual  surface  of  separation.  Let 
a  ring  or  long  bar  magnet  be  cut  into  portions  which  have 
their  ends  carefully  faced  to  be  true  planes,  and  let  these 
abut  against  one  another.  The  force  between  the  faces  may  be 
determined  by  measuring  the  amount  of  pull  which  is  required 
to  draw  them  asunder. 

Measurements  of  the  tractive  force  between  the  parts  of  a 
divided  magnet  were  made  by  Joule,*  who  showed  that  the 
amount  of  the  force  required  to  separate  two  parts  of  a  divided 
magnet  varied  as  the  area  of  cross-section,  and  found  that  the 
tractive  force  might  be  as  great  as  1751b.  per  square  inch. 
Shelf ord  Bidwell,t  using  a  divided  ring  electro-magnet  of  iron, 
found  that  the  weight  which  could  be  sustained  per  square 
centimetre  of  the  cross-section  was  related  to  the  magnetising 
force  in  the  manner  shown  by  Table  XXV.  : — 

Table  XXV. — Tractive  Force  of  a  Divided  Ring  Electro-Magnet. 


Magnetic 

Tractive  force  in 

Magnetic 

Tractive  force  in 

Force 

grammes  weight  per 

Force 

grammes  weight  per 

H. 

square  cm. 

H. 

square  cm. 

3-9 

2,210 

145 

12,800 

57 

3,460 

208 

13,810 

10-3 

5,400 

293 

14,350 

177 

7,530 

362 

14,740 

22-2 

8,440 

427 

15,130 

30-2 

9,215 

465 

15,275 

40 

9,680 

503 

15,365 

78 

11,550 

557 

15,600 

115 

12,170 

585 

15,905 

As  one  gramme  per  square  centimetre  corresponds  to 
0-01 4 21b.  per  square  inch,  the  highest  tractive  force  reached 
in  this  experiment  was  2261b.  per  square  inch.  In  these 
experiments  the  values  of  the  magnetisation  were  not  directly 
observed.  They  may,  however,  be  inferred  from  the  values 
of  the  tractive  force  in  a  manner  which  will  be  explained 
presently. 


*  Phil.  Mag.,  1852,  Vol.  III.,  p.  32,  or  Reprint  of  Papers, 
t  Proo.  Boy.  Soc.,  1886,  Vol.  XL.,  p.  486. 


256 


MAGNETISM    IN    IRON. 


Further  experiments  on  the  same  subject  have  been  made  by 
Bosanquet,*  who  used  bar  magnets,  and  employed  a  small 
induction  coil  (encircling  the  bar  close  to  the  surface  of  division) 
to  determine  the  value  there  of  B  at  the  instant  the  two 
portions  of  the  bar  parted  company  (Fig.  129).  In  this  case 
it  was  possible  to  compare  the  actual  values  of  the  tractive 
force  with  the  values  which  were  to  be  anticipated  from 
the  known  values  of  B.  Bosanquet  has  made  this  com- 
parison, and  has  found  a  fair  agreement  except  in  the  early 
^  stages  of  the  experi- 

ment. When  B  had  any 
value  less  than  about 
5,000  the  observed  trac- 
tive force  was  greater 
than  the  calculated 
force.  This  is  possibly 
to  be  ascribed  in  part 
to  friction  in  the  ap- 
pliance by  which  the 
lower  magnet  was 
guided,  and  in  part  to 
a  supplementary  attrac- 
tion between  the  magne- 
tising coils,  which  was 
then  more  considerable 
than  when  B  was 
greater.  With  an  in- 
duction B  of  18,500 
Bosanquet  observed  a 
tractive  force  equivalent 
to  2071b.  weight  per  square  inch  of  section  of  his  iron  core. 

Probably  the  most  exact  experiments  dealing  with  the 
tractive  force  due  to  magnetisation  are  those  of  Dr.  Taylor 
Jonest,  who  used  an  ellipsoid  of  iron  cut  across  the  middle  of 
its  long  axis,  the  face  of  each  half  being  carefully  polished. 
The  force  required  to  separate  the  polished  surfaces  was 
measured,  under  magnetising  forces  some  of  which  were  strong 
enough  to  raise  the  induction  to  20,000  C.G.S.  units.  The 


Counterpoise 


FIG.  129. — Bosanquet's  Arrangement  for 
Measuring  Magnetic  Traction. 


*  Phil.  Mag.,  1886,  Vol.  XXII.,  p.  535. 
f  Phil.  Mag.,  1895,  Vol.  XXXIX.,  p.  254 


also  1896,  Vol.  XLI.,  p.  153 


LAW  OF  TRACTIVE  FORGE.  257 

experiments  gave  results  in  agreement  with  the  theoretical 
relation  of  tractive  force  to  induction,  which  will  be  stated  in 
the  next  paragraph.  In  a  later  series  of  experiments  Dr. 
Taylor  Jones  verified  the  theory  up  to  inductions  of  40,000. 

§  147.  Relation  of  Tractive  Force  to  Magnetisation. — In 
connection  with  these  experiments  it  is  interesting  to  inquire 
what  is  the  relation  that  theory  would  lead  us  to  anticipate 
between  the  magnetisation  of  the  core  of  a  rod  or  ring  electro- 
magnet, and  the  tractive  force  necessary  to  overcome  magnetic 
attraction  at  the  abutting  faces  if  the  core  is  cut  in  two.  This 
matter  has  been  the  subject  of  some  discussion,*  and  it  appears 
that  a  sufficiently  careful  distinction  has  not  always  been  drawn 
between  different  conditions  which,  to  some  extent,  affect  the 
result.  Consider  the  case  of  an  indefinitely  long  rod,  or  a  ring, 
wound  throughout  with  a  solenoid  which  produces  a  uniform 
magnetic  force  H.  Let  the  intensity  of  magnetisation  be  I  and 
the  induction  B,  as  usual.  Let  the  rod  or  ring  be  cut  across, 
the  cut  faces  be  scraped  to  form  true  planes,  and  placed  in  con- 
tact, so  that  the  whole  behaves,  magnetically,  as  nearly  as 
possible  like  an  undivided  core.  At  the  junction  there  is  an 
indefinitely  narrow  crevasse,  on  each  side  of  which  the  surface 
density  'of  magnetism  is  I.  The  result  of  that  is  (as  was 
shown  in  §  145)  that  the  opposing  surfaces  pull  one  another 
together  with  a  stress  the  amount  of  which  per  square  centi- 
metre of  surface  is  2  TT  I2  in  dynes.  Since  B  =  47r|  +  H  this 

quantity  may  be   written  -i — - — L..     If  the  magnetism  that 

8  7T 

is  dealt  with  is  residual  (that  is  to  say,  if  H  is  zero)  this  is  the 
whole  force  that  must  be  overcome  in  separating  the  surfaces. 
So  that  if  s  is  the  area  of  surface  in  contact  the  whole  tractive 
force  is  in  that  case  equal  to  2  TT  |2s.  But  suppose  H  is  not 
equal  to  zero — in  other  words,  suppose  that  some  current  is 
circulating  in  the  solenoid — then  the  separation  of  the  opposing 
faces  involves  the  movement  through  a  field  H,  in  the  direc- 
tion of  the  field,  of  a  quantity  of  free  magnetism  the  amount 
of  which  (per  centimetre  of  surface)  is  [.  There  is,  therefore,  a 
supplementary  force  required,  the  value  of  which  is  H  I. 

But  this  is  not  necessarily  all     The  solenoid  may  itself  be 

*  See  a  Paper  by  Prof.  S.  P.  Thompson,  Phil.  May.,  1888,  p.  71. 


258  MAGNETISM    IN    IRON. 

wound  in  two  portions  —  one  on  each  part  of  the  divided  core  — 
so  that  the  separation  of  the  core  involves  the  separation  of  the 
two  parts  of  the  solenoid.  In  that  case  we  have  to  exert 
enough  additional  tractive  force  to  overcome  the  attraction  of 
one  coil  on  the  other.  The  amount  of  this  attraction  will 
Depend  on  the  area  of  the  coils.  Take  the  simplest  possible 
case,  that  of  a  solenoid  so  closely  wound  upon  the  core  that  the 
area  of  the  coil  may  be  considered  identical  with  the  area  of 
the  core.  The  two  coils,  considered  alone,  then  behave  like 
magnets  having  poles  whose  surface  density  is  n  C,  where  n  is 
the  number  of  turns  per  centimetre,  and  C  is  the  current.  The 
attraction  between  them,  per  sq.  cm.,  is,  therefore,  27r?i2C2. 
Since  H  is  equal  to  4  TT  n  C,  this  attraction  may  be  written 

U2 

—  We  have  here  a  third  term  which  has  to  be  added  to 
8:r 

the  other  two  in  the  case  considered,  namely,  when  the  sole- 
noid (closely  wound  on  the  core)  is  parted  along  with  the 
core.  It  must  be  borne  in  mind  that  the  second  term  H  I 
occurs  in  this  case,  as  well  as  in  the  case  where  the  solenoid 
remains  undivided,  and  the  two  parts  of  the  core  alone  part 
company.  For  in  the  case  of  a  divided  solenoid  each 
half  of  the  solenoid  pulls  the  opposing  half  core  with  a  force 
which,  per  unit  of  area,  is  2  TT  n  C  I,  or  J  H  I.  There  are 
two  such  forces  to  be  overcome,  namely,  between  the  lower 
core  and  the  upper  solenoid,  and  between  the  lower  solenoid 
and  the  upper  core,  and  the  two  make  up  H  I  as  before. 

In  the  case,  then,  of  a  divided  electro-magnet,  in  which  the 
magnetising  coil  parts  along  with  the  core,  and  in  which  the 
coil  has  no  superfluous  area  (which  would  add  still  further 
to  the  tractive  force),  the  whole  force  is  made  up  of  three 


O7T 

This  may  be  written 


O7T 


_  . 

8;r  V  8n- 

This    is  the  expression  commonly  used  in  calculating  the 
relation  of  the  tractive  force  at  the  cut  to  the  magnetism. 


MEASURING   MAGNETISM    BY    THE   TRACTIVE    FORCE.  259 

In  the  exact  consideration,  however,  of  any  given  case,  the 
particular  disposition  of  the  magnetising  coil  should  be  taken 
account  of.  If  it  is  in  one  length,  or  carried  independently 
of  the  core,  so  that  the  pull  of  its  two  parts  on  one  another 
does  not  have  to  be  overcome,  the  tractive  force  is  less.  If,  on 
the  other  hand,  the  coil  is  separated  along  with  the  core,  and 
has  an  area  larger  than  the  core  itself,  the  force  to  be  overcome 
expressed  per  centimetre  of  the  core  will  be  even  greater  than 

B2 

o^.    In  practice,  especially  when  dealing  with  iron,  the  term 

expressing  the  mutual  attraction  of  the  magnetising  coils  is 
usually  insignificantly  small,  since  B  is  enormous  compared  with 
H,  for  such  values  of  magnetic  force  as  are  usually  employed. 

By  considering  on  general  principles  the  state  of  stress  in  a 
magnetic  medium  which  would  give  rise  to  the  mechanical 
forces  that  are  observed  in  the  magnetic  field,  Maxwell* 
showed  that  where  there  is  no  magnetisation!  there  is  a  tension 

LJ2 

along  the  lines  of  force  equal  to    ~ .     Within  the  indefinitely 

8  7T 

thin  crevasse  of  air  which  separates  the  two  opposed  faces  of 
a  cut  magnet  there  is  no  magnetisation,  and  the  value  of  H 
there  is  that  of  B  in  the  substance  of  the  metal.  This  ex- 
pression for  the  tractive  force  between  the  faces  is  therefore 
equivalent  to  the  expression  which  has  been  deduced  above 

B2 

in  a  more  elementary  fashion,  namely, 

8  TT 

§  148.  Determination  of  Magnetisation  by  Measuring  the 
Tractive  Force. — Once  a  relationship  is  established  between 
the  tractive  force  and  B  or  I,  measurements  of  the  tractive 
force  may  be  resorted  to  as  a  means  of  determining  magnetisa- 
tion. This  gives  a  fourth  type  of  magnetic  measurements, 
distinct  from  the  ballistic,  the  direct  magnetometric,  and  the 
optical  methods  which  have  been  described  in  earlier  chapters. 
The  traction  method  of  determining  magnetisation  has  been 
used  with  good  effect  by  Bidwell,  who  determined  curves  of 
magnetisation  by  observing  the  relation  of  the  tractive  force 
required  to  separate  the  halves  of  a  divided  iron  ring  to  the 

*"  Electricity  and  Magnetism,"  Vol.  II.,  §§  641-646. 
c.  ct«.,§643. 

82 


2GO  MAGNETISM    IN    IRON. 

intensity  of  magnetising  force  produced  by  a  divided  solenoid 
with  which  the  halves  of  the  ring  were  wound.*  In  reducing 
the  results  he  used  27r|2+H  I  as  the  equivalent  of  the 
tractive  force.  In  the  actual  circumstances  of  his  experiment 

I_J2  D2 

the  addition  of  the  third  term  —  (making  — in   all)   would 

OTT  STT 

have  been  proper  ;f  but  the  effect  of  this  change  on  the  nume- 
rical values  of  B  or  of  I  deduced  from  his  experiments  is  quite 
trifling.  His  magnetic  forces  ranged  up  to  585,  and  produced 
at  their  highest  value  an  amount  of  attraction  from  which  I 
was  calculated  to  be  1,530,  B  19,820,  and  ^  33-94 

More  recently  Prof.  S.  P.  Thompson  has  proposed  the  use  of 
a  simple  traction-measuring  instrument  as  a  workshop  appli- 
ance for  determining  permeabilities. §  This  "  permeameter," 
as  he  terms  it,  is  shown  in  Fig.  130.  The  specimen  to  be 
tested  is  a  rod  which  slips  through  a  hole  in  the  top  of  a  sub- 
stantial iron  yoke,  and  through  a  bobbin  on  which  the  mag- 
netising coil  is  wound.  The  lower  end  of  the  sample  is  faced 
true,  and  rests  on  a  part  of  the  yoke  which  is  also  scraped  to 
have  a  truly  plane  surface.  The  force  required  to  detach  the 
sample  from  the  surface  of  the  yoke  is  measured  by  means  of  a 
spring  balance.  In  consideration  of  the  fact  that  the  magnetising 

(B  -  H)2 
coil  is  left  in  situ,  Prof.  Thompson  takes  v —  as  the  quan- 

STT 

tity  that  represents  the  tractive  force,  and  from  this  the  prac- 
tical rules  are  derived  : — 

Pull  in  Ibs.  _  (B  ~  H)2  x  s  (square  centimetres) 

o      oo  A  *      /  Pull  in  Ibs.       LI 

or.  B  =  3344  A  / +  H, 

v     s  111  sq.  cms. 

B=i3nV;M™I  +  H. 

v    s  m  sq.  inches 

It  may  be  questioned  whether  the  place  chosen  for  the  plane 
of  contact  in  the  "permeameter"  is  the  best  possible.  The 

*  Proc.  Boy.  Soc.,  1886,  Vol.  XL. 

t  As  Mr.  Bidwell  has  himself  remarked,  Phil.  Mag.,  1390,  XXIX.,  p.  440. 

J  Dr.  Taylor  Jones  (Phil.  Mag.,  1896,  Vol.  XLL,  p.  165)  has  made  use  of 
the  measured  tractive  force  to  determine  the  induction  in  very  strong  fif Ids. 
Using  a  magnet  designed  by  du  Bois  to  magnetise  a  pin-->ll  "  isthmus"  of 
iron  he  has  in  this  way  found  a  val  .e  of  B  as  high  as  74,'tOO  C  G,S.  units, 

§  Jour.  Soc.  Arts,  Sept.  12.  1890. 


THE   PERMEAMETEU. 


261 


: ; — Spring  balance 


distribution  of  induction  is  rather  unequal  where  the  bar  meets 
the  yoke,  and  better  results  might  be  obtained  by  making  the 
sample  in  two  pieces  with  a  plane  of  contact  at  the  middle. 
Apart  from  this,  however,  no  traction  method  can  be  regarded  as 
a  very  satisfactory  means  of  examining  the  magnetic  quality  of 
a  metal.  The  presence  of  tensile  stress  itself  affects  the  quality 
which  is  undergoing  measurement,  and,  as  will  be  shown  later, 
a  divided  rod  or  ring  does  not  behave  magnetically  quite  like 
a  whole  rod,  even  when  the  ends  are  surfaced  as  carefully 

as  is  practicable.  The  existence 
of  a  cut  lessens  the  permeability 
of  the  piece.*  The  traction 
method  is  at  the  best  inexact,  but 
it  affords  a  ready  means  of  making 
rough  measurements,  especially 
for  purposes  of  comparison. 

A  more  elaborate  apparatus  for 
determining  magnetisation  by  aid 
of  the  tractive  force  is  the  mag- 
A  netic  balance  of  Dr.  du  Bois,  in 
which  the  magnetic  circuit,  of 
which  the  rod  under  examination 
forms  part,  has  a  gap  in  the  yoke, 
and  the  tractive  force  across  this 
gap  is  measured.  This  appa- 
ratus will  be  referred  to  more 
particularly  in  the  Chapter 
on  Practical  Magnetic  Testing. 
The  author  has  also  designed 
a  simple  form  of  magnetic 
balance  which  compares,  for  a  single  value  of  H,  the  value  of  B 
acquired  by  one  rod  with  that  acquired  by  a  standard  rod  in 
which  the  relation  of  B  to  H  is  already  known.  In  this 
instrument,  which  will  also  be  referred  to  more  particularly  in 
the  last  Chapter,  the  traction  test  is  used  merely  as  a  means 
of  comparison,  no  attempt  being  made  to  measure  it  absolutely 
or  to  determine  the  induction  directly  from  the  absolute  value 
of  the  force.  The  author  finds  that  for  comparison  of  one  rod 
with  another  the  tractive  method  answers  well. 
~*  Phil.  Mag.,  Sept.,  1888. 


Wires  that 
bring  the 
Electric  current 


FIG.  130.— The  Permeameter. 


CHAPTER  X. 


THE  MAGNETIC  CIRCUIT. 

§  149.  The  Magnetic  Circuit. — For  many  purposes,  the  most 
convenient  way  of  treating  the  magnetisation  of  iron  is  to  con- 
sider what  is  happening  at  a  point  within  the  metal.  This  is, 
in  fact,  the  basis  on  which  our  exposition  of  the  subject  in 
earlier  chapters  has  been  developed.  We  have  learnt  to  con- 
ceive of  a  magnetic  force  H  acting  in  a  definite  direction  at 
the  point  considered,  and  also  of  a  magnetic  induction  B  at  the 
point.  If  the  material  is  isotropic,  and  has  no  residual  mag- 
netism superposed  upon  the  magnetism  which  H  induces,  the 
direction  of  B  is  the  same  as  that  of  H.  The  ratio  of  B  to  H 
is  the  permeability  /A.  Passing  from  point  to  point  of  the 
metal,  we  may  in  certain  cases  find  that  H  and  B  do  not 
change  ;  more  generally  they  do  change.  Thus,  in  a  uniformly 
wound  circular  ring  magnet,  of  uniform  section  and  material, 
H  has  the  same  value  at  all  points  on  any  circle  co-axial 
with  the  ring.  In  a  long  straight  bar  magnet  the  value  of  H 
is  nearly  uniform,  except  in  the  neighbourhood  of  the  ends. 
Whether  H  be  uniform  or  not,  it  has  a  single  definite  value 
and  definite  direction  at  each  point,  and  the  same  is  true  of  B. 
At  points  where  there  is  no  magnetisable  substance,  the  value 
and  direction  of  B  are  the  same  as  the  value  and  direction  of  H  ; 
this  applies,  for  instance,  to  all  points  in  air.  The  value  of  H  at 
any  point  is  determined  by  finding  the  resultant  of  the  force 
produced  at  that  point  by  (1)  all  the  conducting  circuits,  and  (2) 
all  the  free  magnetism  in  the  neighbourhood  ;  that  is,  by  finding 
the  resultant  mechanical  force  which  would  be  felt  by  a  unit 
pole  of  free  magnetism  if  placed  at  the  point  in  question. 


THE    MAGNETIC   CIRCUIT.  263 

From  this  point  of  view,  when  our  object  is  to  discuss  the 
magnetisation  of  a  piece  of  metal,  we  have  first  to  consider 
what  is  the  value  of  H  at  each  point  within  the  piece.  Thus, 
in  dealing  with  a  uniformly-wound  ring,  we  treat  the  case  by 
finding  that  the  magnetic  force  H  is  4  TT  C  n,  when  C  is  the  cur- 
rent and  n  is  the  number  of  turns  in  the  magnetising  coil  per 
centimetre  of  the  ring's  length.  And  in  dealing  with  a  uni- 
formly-wound rod,  we  find  H  to  be  4  TT  C  n  minus  a  certain 
quantity  due  to  the  free  magnetism  at  and  about  the  ends, 
which  becomes  unimportant  when  the  rod  is  exceedingly  long. 
Many  problems  in  magnetism  are  best  treated  in  this  way, 
namely,  by  considering  the  condition  of  things  at  individual 
points  in  the  magnetised  piece. 

But  there  is  another  way  of  regarding  the  matter,  not  in  the 
least  antagonistic  to  this,  but  sometimes  more  convenient. 
Instead  of  thinking  about  what  happens  at  individual  points, 
we  may  view  the  magnetism  of  the  piece  as  a  whole,  by 
considering  what  is  called  the  magnetic  circuit.  This  is  the 
method  which  has  been  applied  by  J.  and  E.  Hopkinson*  and 
by  Kapp,f  to  pre-determine  the  magnetism  of  dynamos.  Its 
applicability  to  dynamos  and  transformers  gives  it  peculiar  im- 
portance on  the  practical  side  ;  moreover,  apart  from  that,  the 
conception  of  the  magnetic  circuit  has  much  interest  as  an 
alternative  standpoint  from  which  the  facts  of  electro -magnetism 
may  be  viewed,  and  as  suggesting  methods  of  experimental 
enquiry. 


§  150.  Tubes  of  Magnetic  Induction.  Definition  of  Mag- 
netic Flux  and  of  a  Perfect  Magnetic  Circuit. — The  lines  of 
magnetic  induction,  as  has  been  already  pointed  out  (§  14),  are 
continuous  through  space,  whether  the  space  be  filled  with 
magnetisable  or  non-magnetisable  substance,  or  partly  with  one 
and  partly  with  the  other.  There  is  no  discontinuity  of  B — 
no  sudden  change  in  its  value  or  direction — when  the  lines 
pass  from  metal  to  air  or  from  air  to  metal.  Each  line  of  in- 
duction is  a  continuous  curve;  moreover,  it  is  a  closed  curve 
— that  is  to  say,  if  traced  along  its  whole  course  it  returns 
to  the  point  at  which  the  tracing  began.  We  may  conceive  of 

*  Phil.  Trans.,  1886,  p.  331.  t  Jour.  Soc.  Tel.  Eng.,  1886,  p.  518. 


264  MAGNETISM    IN    IRON. 

all  space  as  filled  with  sheafs  of  lines  of  induction,  or  (which 
is  the  same  thing  in  other  words)  as  partitioned  into  tubes,  the 
boundaries  of  which  are  formed  by  lines  of  induction.  Every 
such  tube  contains  a  number  of  lines  of  induction,  and  if  we 
follow  the  tube  along  its  whole  length  until  -it  returns  into 
itself  we  find  everywhere  the  same  number  of  lines  of  induction 
in  it.  We  may  take  a  large  sheaf  or  a  small  one  to  constitute 
the  tube,  but,  whatever  be  the  number  of  lines  in  it  to  start 
with,  the  same  number  is  present  at  every  part  of  its  length. 
Its  cross-section  may  vary ;  the  tube  may  widen  or  contract  from 
place  to  place  along  its  length,  but  if  this  happens  it  is  by  the 
lines  spreading  out  or  coming  closer ;  the  number  of  the  lines 
does  not  change.  At  places  where  the  induction  B  is  strong, 
the  tube  is  contracted  ;  at  places  where  the  induction  is  weak, 
the  tube  is  expanded.  But  if  we  take  any  cross-section  (s) 
of  the  tube  perpendicular  to  the  direction  of  B,  the  product 
B  s  (or,  to  be  more  exact,  the  surface-integral  fBds  taken 
over  the  section,  since  B  is  not  necessarily  the  same  over  all 
parts  of  s*)  is  a  constant  quantity  for  any  one  tube.  At 
any  sections  s  and  s',  the  values  of  the  induction  B  and 
B'  are  such  that  /  B  d  s  =/  B'  d  s'.  It  is  convenient  to  have 
a  name  for  this  constant  quantity,  which  is  the  whole  number 
of  lines  of  magnetic  induction  in  the  tube.  Following  the 
usage  of  several  recent  writers  we  shall  call  it  the  magnetic  flux 
in  the  tube. 

Any  tube  of  magnetic  induction,  considered  as  a  whole — 
that  is  to  say,  considered  as  a  circuit  which  returns  into  itself — 
may  be  called  a  perfect  magnetic  circuit.  The  perfect  magnetic 
circuit  is  analogous  to  a  perfectly  insulated  electric  circuit  con- 
ducting a  current.  The  lines  of  induction  correspond  in  this 
analogy  to  lines  of  flow  of  current.  The  cross-section  of  the 
conductor  may  vary  from  place  to  place,  but  the  current 
density  varies  in  inverse  proportion  to  the  cross-section,  so 
that  the  product  of  current  density  into  area  of  cross-section 
— which  is  simply  the  whole  current — is  constant  at  all  sections, 
just  as  the  flux  Bs  is  constant  in  the  perfect  magnetic  circuit. 

*  The  cross-section,  over  which  this  integral  is  calculated,  is  taken  BO 
that  every  element  of  the  surface  is  perpendicular  to  the  lines  of  B  which 
cut  it.  Thus,  if  the  lines  of  B  in  the  tube  are  not  parallel,  the  surface 
forming  the  cross-section  will  be  curved. 


MAGNETOMOTIVE   FORCE.  265 

§  151.  Imperfect  Magnetic  Circuit. — An  imperfectly  insu- 
lated electric  circuit  allows  some  of  the  lines  of  flow  to  enter 
it  or  to  leave  it  through  the  sides.  We  have  the  magnetic 
analogue  of  this  when  we  have  to  deal  with  the  magnetisation 
of  a  material  ring  of  any  form,  in  which  the  sides  of  the  ring 
do  not  coincide  with  the  sides  cf  a  tube  of  induction.  This 
means  that  there  are  places  where  some  of  the  lines  of  induc- 
tion leak  out,  so  to  speak,  from  the  substance  of  the  ring 
through  its  sides  into  the  surrounding  medium.  It  is  often 
convenient,  especially  when  the  greater  part  of  the  whole  flux 
remains  in  the  ring,  still  to  speak  of  such  a  ring  as  a  magnetic 
circuit.  We  shall  distinguish  it  from  a  true  tube  of  induction 
by  calling  this  leaky  ring  an  imperfect  magnetic  circuit.  It  is 
imperfect,  inasmuch  as  it  leaves  out  those  portions  of  the  sur- 
rounding medium  through  which  some  of  the  lines  of  induction 
stray,  the  inclusion  of  which  would  be  necessary  in  order  to  mako 
the  tubes  of  induction  complete.  Examples  of  imperfect  cir- 
cuits will  be  given  presently. 

§  152.  Line-Integral  of  Magnetic  Force,  or  Magnetomotive 
Force. — We  have  now  to  express  the  relation  of  the  magnetic 
flux  in  a  perfect  magnetic  circuit  to  the  whole  magnetising 
agency  acting  on  the  circuit,  just  as  in  a  perfectly  insulated 
electric  circuit  we  express  the  relation  of  the  current  to  the  whole 
electromotive  force  that  is  operative  throughout  the  circuit. 

We  have  in  the  magnetic  circuit  an  agent  to  which  (when 
we  are  dealing  with  induced  magnetism)  the  magnetic  flux  is 
due,  which  corresponds  to  the  electromotive  force  of  the  electric 
circuit.  To  this  agent  Bosanquet*  has  given  the  name  of 
magnetomotive  force. 

One  way  of  defining  the  electromotive  force  of  an  electric 
circuit  is  to  say  that  the  electromotive  force  is  the  amount  of 
work  which  would  be  done  in  carrying  unit  quantity  of  elec- 
tricity completely  round  the  circuit. 

In  the  same  way  we  may  define  the  magnetomotive  force  of 
a  magnetic  circuit  as  the  amount  of  work  which  would  be  done 
in  carrying  a  unit  magnetic  pole  completely  round  the  circuit. 
At  any  point  of  its  path  the  unit  pole  is  acted  on  by  a  mechanical 
force  which  is  equal  to  and  in  the  direction  of  the  magnetic 
*  Bosanquet,  Phil.  Mag.,  1883,  Vol.  XV.,  p.  205. 


266  MAGNETISM    IN    IRON. 

force  H,  and  it  is  against  this  mechanical  force  that  the  work 
is  done. 

Another  name  for  the  same  quantity  is  the  Line-Integral  of 
Magnetic  Force,  taken  round  the  circuit.*  Conceive  the  path 
along  which  the  unit  pole  is  moved  to  be  made  up  of  a  great 
many  short  pieces,  any  one  of  which  is  so  short  as  to  be  sensibly 
straight  and  to  have  a  sensibly  uniform  value  of  H  from  end 
to  end  of  it.  Let  the  length  of  any  short  piece  be  3  /,  and  let 
its  inclination  to  the  direction  of  H  be  e.  Then  the  work  done 
in  moving  the  unit  pole  along  this  short  piece  of  the  path  is 
measured  by  the  product  of  the  length  of  the  path  (S  fc)  into 
the  component  of  the  force  H  along  the  path ;  that  is  to  say, 
it  is  H  cos  €  8  I.  The  whole  work  done  in  moving  a  unit  pole 
along  the  path  is  got  by  summing  up  the  work  done  at  each 
short  piece  ;  that  is  to  say,  it  is  2  H  cos  €  8  I,  or/H  cos  e  d  I 
when  the  elements  into  which  the  path  is  divided  are  indefinitely 
numerous  and  indefinitely  short.  The  expression/  H  cos  edl 
is  the  line-integral  of  the  magnetic  force  along  the  path. 

We  may  integrate  the  magnetic  force  in  this  manner  along 
any  curve  whatsoever.  The  term  line-integral  of  magnetic 
force  is  not  in  the  least  restricted  to  cases  in  which  the 
integration  takes  place  round  a  magnetic  circuit.  Let  the 
path  through  which  the  unit  pole  is  supposed  to  be  carried 
extend  through  space  in  any  manner,  the  line-integral, 
namely,  /  H  cos  €  d  I,  measures  the  work  done  in  carrying  the 
pole  along  it. 

In  cases  where  the  direction  of  the  line  coincides  at  all  points 
of  its  course  with  the  direction  of  H,  cos  e  is  everywhere  unity, 
and  the  expression  for  the  line-integral  of  the  magnetic  force 
becomes/  H  d  I.  This  is  generally!  the  case  when  the  line  in 
question  is  a  line  of  magnetic  induction,  which  it  may  always 
be  when  the  line-integral  of  magnetic  force  is  calculated  for 
a  perfect  magnetic  circuit. 

§  153.  Value  of  the  Line-Integral  of  Magnetic  Force. — 
When  the  integration  is  extended  all  along  any  closed  curve — 
in  other  words,  when  the  imaginary  unit  magnetic  pole  makes 

*  Maxwell,  "El.  and  Mag.,"  Vol.  II.,  §401. 

t  Namely,  when  the  medium  is  isotropic  and  has  no  residue  of  previous 
magnetisation  in  a  direction  inclined  to  the  direction  of  H. 


LINE-INTEGRAL    OP    MAGNETIC    FORCE.  267 

a  complete  journey  along  any  path  which  returns  into  itself — it 
may  be  shown  that  the  value  of  the  line-integral  of  magnetic  force 
admits  of  very  easy  calculation.  If  the  curve  along  which  it  is 
reckoned  does  not  thread  its  way  through  any  circuit  in  which 
a  current  is  flowing,  then  the  value  of  the  line-integral  of  mag- 
netic force  along  the  closed  curve  is  zero.  If  the  curve  does 
thread  its  way  once  through  a  circuit  in  which  a  current  C  is 
flowing,  then  the  value  of  the  line-integral  of  magnetic  force 
along  the  closed  curve  is  4  TT  C ;  and  if  the  curve  threads  its 
way  N  times  through  such  a  circuit,  the  value  of  the  line- 
integral  is  4  TT  C  N.  For,  example,  if  the  line  along  which  the 
line-integral  of  magnetic  force  is  reckoned  is  any  closed  curve 
which  is  threaded  through  the  interior  of  a  coil  of  N  turns,  the 
line-integral  is  4  TT  C  N,  for  the  line  is  interlinked  with  the 
current  circuit  as  many  times  as  there  are  turns  in  the  coil. 

The  principle  that  the  line-integral  of  magnetic  force  is 
equal  to  4  TT  C  N,  when  taken  along  any  closed  curve  is  an  abso- 
lutely general  one.  It  is  true  whatever  be  the  position  and 
direction  of  the  curve,  whether  it  lie  along  a  line  of  force  or  no, 
and  whether  it  lie  wholly  or  partly  in  a  non-magnetisable  sub- 
stance, such  as  air,  or  wholly  or  partly  in  a  magnetisable  sub- 
stance, such  as  iron.  If  the  closed  curve  threads  through  more 
circuits  than  one,  the  sum  of  the  terms  4  TT  C  N  is  to  be 
taken. 

Two  simple  cases  will  serve  as  instances.  Suppose  we  ha^e 
a  uniform  solenoid  of  n  turns  per  centimetre,  and  I  centimetres 
long.  Let  the  ends  be  bent  together  so  that  it  forms  a  closed 
ring.  The  length  of  a  closed  curve  in  the  centre  of  the  solenoid 
is  I.  The  magnetic  force  H  is  uniform  all  along  that  line,  and 
is  equal  to  4  TT  C  n.  The  value  of  /  H  d  I  is,  therefore,  H  I  or 
4  TT  C  n  I,  or  4  TT  C  N,  since  N  the  whole  number  of  turns  =  n  I. 

Again,  consider  the  magnetic  force  around  a  long  straight 
conductor  (the  remainder  of  the  circuit  being  supposed  to  lie  so 
far  off  as  to  be  uninfluential)  and  integrate  /  H  d  I  along  the 
circumference  of  a  circle  of  which  the  conductor  is  axis.  The 

2  f1 

force  at  any  distance  r  from  the  axis  of  the  conductor  is  — _. 

r 

This  is  uniform  throughout  the  circular  path,  and  is  in  the 
direction  of  the  path.  The  length  of  the  path  is  2  TT  r.  The 
line-integral  of  magnetic  force  round  the  path  is,  therefore, 


268  MAGNETISM   IN 

2  C 

—  x  2  TT  r  or  4  ?r  C.     In  this  case  the  path  along  which  the 

line-integral  is  taken  is  interlinked  with  the  circuit  only  once. 

The  principle  set  forth  in  this  paragraph  may  be  stated 
thus  : — The  line-integral  of  magnetic  force  along  any  closed 
curve  is  equal  to  O^TT,  or  1-2566,  into  the  number  of  ampere- 
turns  in  the  coil  or  coils  which  are  threaded  by  the  curve. 

§  154.  Equation  of  the  Magnetic  Circuit. — Returning  now 
to  the  case  of  a  perfect  magnetic  circuit,  we  have  to  consider 
the  connection  between  the  magnetomotive  force  or  line-integral 
of  magnetic  force  along  the  circuit  and  the  magnetic  flux. 
Suppose  the  circuit  to  be  divided  up  into  a  number  of  tubes 
of  induction,  in  each  of  which  the  cross-section  is  small,  so 
that  B  and  H  may  be  taken  as  uniform  over  any  one  cross 
section  of  the  (small)  tube.  The  relation  which  we  establish 
for  each  small  tube  may  easily  be  extended  to  apply  to  the 
whole  magnetic  circuit,  which  is  built  up  of  such  small  tubes 
placed  side  by  side.  Let  s  be  the  area  of  cross-section  at  any 
part  of  the  small  tube,  and  B  the  magnetic  induction  there. 

The  flux  in  the  tube  is  B  s.     If  /*  be  the  permeability  of  the 

p 
substance,  the  magnetic  force  H  at  the  same  place  is  — ;  hence, 

flux     B     ,, 
—  =  — =  H. 

fl,8          /* 

Multiply  each  side  by  an  indefinitely  short  length  of  the  tube 
dl— 

fluxx— =Hd£ 
pi 

Integrate  both  sides,  remembering  that  the  flux  is  constant  at 
all  sections  ; 

flux  x  I  —  =  IHdl  =  magnetomotive  force, 

J  ft.9      J 

when  the  integration  is  extended  round    the  whole  circuit ; 

magnetomotive  force 
hence,  flux=  "  "  r^l 

J~jTs 
The  meaning  of  the  denominator  may  be  most  readily  seen 

if  we  write  p  for  _  and  call  />  the  specific  magnetic  resistance  of 


EQUATION    OF   THE    MAGNETIC    CIRCUIT.  269 

the  substance.    Then  p       is  evidently  the  magnetic  resistance 

I 

of  that  portion  of  the  magnetic  circuit  which  has  the  length  d  I 
and  the  cross  section  s.  The  idea  of  magnetic  resistance  is  intro- 
duced here  in  a  sense  strictly  analogous  to  the  idea  of  electric 
resistance  in  the  electric  circuit.  The  specific  magnetic  resist- 
ance p  is  the  analogue  of  the  specific  resistance  to  conduction 
— namely,  the  resistance  of  a  piece  of  the  conductor  of  unit 

length  and  unit  area  of   cross-section.     The  quantity  IL —  is» 

J    s 

simply  the  sum  of  the  resistances  of  successive  short  portions 
of  the  length  of  the  circuit.      We  may,  therefore,  write  the 
equation  of  the  perfect  magnetic  circuit  thus — 
fl      _  magnetomotive  force 

magnetic  resistance  of  the  circuit* 

which  is  the  magnetic  analogue  of  the  familiar  equation  of 
conduction — 

.  electromotive  force 

conduction  resistance  of  circuit" 

There  is,  however,  this  reservation  to  be  borne  in  mind  in 
pursuing  the  analogy.  In  the  conduction  circuit  the  specific 
resistance  of  the  material  is  not  a  function  of  the  current — that 
is  to  say,  its  value  is  independent  of  the  amount  of  the 
current.  In  the  magnetic  circuit  p  and  /x  are  functions  of  the 
flux,  for  they  depend  on  the  value  of  B.  More  than  that, 
they  may  have  many  possible  values  even  when  the  value  of 
B  is  assigned,  for  they  depend  not  only  on  the  existing  magnetic 
induction,  but  on  the  previous  magnetic  history  of  the  piece. 
But  the  equation  of  the  magnetic  circuit  will  be  correct  and 
intelligible  if  we  define  JJL  as  nothing  more  or  less  than  the  value 

D 

which  the  quotient  _  happens  to  have  at  that  place  in   the 
H 

circuit  to  which  reference  is  made ;  and  if  we  define  p  as  the 

LJ 

reciprocal  of  that  quantity,  or  _-,  we  may  have  a  magnetic 

B 

circuit  in  which  there  is  no  magnetomotive  force,  but  in  which 
there  is  (residual)  magnetic  flux.  In  that  case  the  "  magnetic 
resistance  "  of  the  circuit  must  vanish,  and  the  mean  value  of 
p  must  be  zero.  We  may  even  have  a  magnetic  circuit  in 


270  MAGNETISM    IN    IRON. 

which  the  direction  of  the  flux  is  (on  account  of  past  mag- 
netisation) opposite  to  the  direction  of  the  magnetomotive 
force,  which  implies  a  negative  value  of  p  and  of  p. 

In  most  of  the  cases  to  which  the  conception  of  the  magnetic 
circuit  may  be  usefully  applied,  the  effects  of  previous  magneti- 
sations are  absent  or  negligible,  so  that  the  values  of  /A  which 
are  to  be  used  are  the  permeabilities  which  are  derived  from 
the  ordinary  curve  of  magnetisation  (for  the  particular  material 
of  the  circuit)  —  that  is  to  say,  from  the  curve  which  expresses 
the  relation  B  to  H  when  H  is  progressively  increased  from 
zero  and  the  metal  is  free  of  magnetism  to  begin  with. 

In  many  instances  the  circuit  may  be  treated  as  (very  ap- 
proximately) made  up  of  a  series  of  portions,  in  any  one  of 
which  /x  is  constant  and  s  is  constant.  Thus,  calling  ^  the 
length  of  one  of  these  portions,  /^  its  permeability,  and  sl  its 
cross-sectional  area,  12  the  length  of  the  next,  /^2  its  permea- 
bility, and  s2  its  sectional  area,  and  so  on,  we  have 

^      _    magnetomotive  force 


as  many  terms  being  taken  in  the  denominator  as  are  needed 
to  complete  the  circuit. 

And  if  the  object  is  to  express  the  value  of  the  induction  at 
any  place  in  the  circuit  in  terms  of  the  magnetomotive  force, 
we  have  only  to  divide  the  flux  by  the  area  of  cross-section 
there.  Thus,  if  it  is  wished  to  express  BI}  the  induction  in 
the  first  portion  of  the  circuit,  where  the  area  of  section  is  sv 
we  have 

D  _flux_    magnetomotive  force 


ft      /*2     S2      /*3     S3 

Or,  again,  if  what  is  wanted  be  to  calculate  the  number  of 
ampere  turns  which  are  required  to  produce  a  stated  magnetic 
flux  in  a  magnetic  circuit  made  up  of  a  series  of  portions  of 
which  the  lengths,  sections,  and  permeabilities  are  known,  we 
may  find  the  magnetomotive  force  from  the  formula 

magnetomotive  force  =  flux  x    (  —  L_  +  —  i_  +  _JL_  +  &c.  Y 

\Pl'l       /V2      /*3S3  / 


EXAMPLES    OF   MAGNETIC    CIRCUITS.  271 

and  then  find  the  number  cf  ampere  turns  by  dividing  the 
magnetomotive  force  by  (Mr.  This  is,  in  effect,  the  problem 
which  is  attacked  in  calculating  the  winding  of  the  field- 
magnets  of  a  dynamo.  The  problem  is  analogous  to  that 
of  finding  the  electromotive  force  necessary  to  drive  a  stated 
current  through  a  circuit  composed  of  a  series  of  conductors  of 
which  the  specific  resistances,  the  lengths,  and  the  cross-sections, 
are  assigned. 

§155.  Particular  Cases:  Continuous  Ring  wound  uni- 
formly and  otherwise.  —  The  utility  of  the  idea  of  the  magnetic 
circuit  will  be  apparent  when  we  consider  one  or  two  examples. 
Take  first  the  case,  already  familiar,  of  a  uniform  ring 
uniformly  wound  with  a  magnetising  coil  of  N  turns.  Let  I  be 
the  length  of  the  ring,  measured  round  any  circle  within  the 
ring  parallel  to  the  sides.  The  magnetic  force  at  all  points  of 

such  a  circle  is  -  ,  and  the  line-integral  of   this,  or  the 

6 

magnetomotive  force,  is  4  TT  C  N.  If  s  be  the  area  of  cross- 
section,  the  magnetic  resistance  of  the  ring  is  —  ,  and  the  flux, 

116 

which  is  equal  to  the  magnetomotive  force  divided  by  the 
resistance,  is 

47I-CN 


We   might,  of  course,   have  derived  this  expression  for  the 
flux  otherwise,  namely  :  — 


L 

The  line-integral  of  magnetic  force  has  the  same  value  for 
all  lines  that  thread  through  the  magnetising  coil.  Moreover, 
the  magnetic  force  H  is  itself  constant  at  all  points  of  the 
circle  I,  parallel  to  the  sides  of  the  ring  ;  so  that  the  line- 
integral  is  H  L  To  compare  the  values  of  H  at  different 
points  in  the  substance  of  the  ring,  at  distances  rv  r2,  &c., 
from  the  axis  of  the  ring,  we  have  Hx  ^i  =  H2  Z2,  ^  =  2  TT  rlt 
and  Z2  =  27rr2;  hence,  H1r1  =  H2r2.  In  other  words,  the 
magnetic  force  due  to  uniform  winding  on  a  uniform  circular 


272  MAGNETISE    IN    IRON. 

ring  varies  across  any  section  in  inverse  proportion  to  the 
distance  of  the  point  from  the  axis  of  the  ring.  (See  §  57, 
ante.) 

In  the  case  of  a  uniformly-wound  uniform  ring  there  is  no 
special  advantage  in  applying  the  conception  of  the  magnetic 
circuit.  The  results  to  which  it  leads  are  obtained,  with  no 
less  ease,  by  considering  the  magnetisation  and  magnetic  force 
at  any  individual  point  of  the  metal.  But  it  should  be  noted 
that  the  conception  of  the  magnetic  circuit  makes  it  possible 
to  avoid  any  use  of,  or  reference  to,  the  quantity  H.  We  have 
derived  the  notion  of  magnetomotive  force  from  that  of  mag- 
netic force,  by  taking  the  line-integral  of  H  round  the  magnetic 
circuit.  But  that  is  by  no  means  a  necessary  order  of  ideas ; 
nor  is  the  notion  of  H  indispensable  in  the  treatment  of  the 
subject.  The  magnetomotive  force  may  be  defined  without 
reference  to  it,  and  the  flux  may  be  stated  in  terms  of  the 
magnetomotive  force  and  magnetic  resistance,  so  that  all  use  of 
H  may  be  excluded.  It  is  even  thsoretically  possible  to  treat 
all  cases  of  magnetisation  in  the  same  way.  With  a  magnetised 
bar,  for  instance,  the  magnetic  circuit  is  completed  through 
the  surrounding  non-magnetic  medium,  and  a  sufficiently 
powerful  analysis  might  determine  the  resistance  of  the 
circuit,  and  so  allow  the  relation  of  magnetic  flux  to  mag- 
netomotive force  to  be  treated  without  any  allusion  to  the 
magnetic  force  at  individual  points  of  the  bar.  But  to 
apply  this  method  universally,  though  theoretically  possible, 
is  quite  impracticable ;  and  there  are  very  many  problems 
in  regard  to  which  the  older  modes  of  viewing  the  subject, 
described  in  earlier  chapters,  are  infinitely  more  convenient. 
The  student  must  not  think  to  abandon  the  consideration 
of  magnetic  force  and  magnetisation  at  individual  points 
because  he  finds  that  the  notion  of  the  magnetic  circuit 
is  remarkably  useful  in  certain  cases,  and  has,  in  theory,  no 
limits  to  its  application.  Its  real  value  lies  in  the  fact  that 
Dy  its  help  problems  which  would  otherwise  be  intractable 
may  be  solved  with  sufficient  exactness  for  practical  purposes. 
To  trace,  for  example,  from  point  to  point  in  the  core  of  a 
transformer  or  the  field  magnets  of  a  dynamo  the  value  of  H, 
and  so  determine  the  magnetisation,  would  be  a  task  the  diffi- 
culty of  which  would  be  prohibitive.  But  by  applying  in  such 


RING   WOUND   NON -UNIFORMLY.  273 

cases  the  method  of  the  magnetic  circuit,  a  solution  is  readily 
arrived  at — not,  indeed,  a  rigorous  solution,  but  one  that  satis- 
fies the  requirements  of  the  electrical  engineer. 

In  the  case  dealt  with  above — that  of  a  uniform  ring  uni- 
formly wound — the  metal  of  the  ring  forms  a  perfect  magnetic 
circuit.  None  of  the  lines  of  induction  stray  into  surrounding 
space ;  the  ring  itself  is  a  tube  of  induction,  and  the  flux  is 
constant  at  all  cross  sections. 

Suppose,  however,  that,  instead  of  being  uniformly  wound, 
part  of  the  ring,  Q,  is  bare  and  the  magnetising  coil  is  heaped  up 


Fia.  131. 

on  the  other  part  P  (Fig.  131 ).  In  that  case  the  flux  through  P  is 
greater  than  the  flux  through  Q,  for  some  of  the  lines  of  induction 
which  thread  through  the  coil  close  themselves  by  passing  not 
through  the  bare  part  of  the  ring  but  through  surrounding  space 
in  the  manner  indicated  by  the  dotted  lines.  The  ring  is  now 
an  imperfect  magnetic  circuit.  If,  however,  the  material  is  very 
permeable,  like  soft  wrought  iron  (the  magnetic  permeability  of 
which,  when  not  too  strongly  magnetised,  is  some  two  or  three 
thousand  times  as  great  as  permeability  of  air),  and  if  the  ring 
is  short — that  is  to  say,  if  its  diameter  is  not  too  great  in  com- 
parison with  the  dimensions  of  its  section — this  leakage  of  lines 
of  induction  into  surrounding  space  will  take  place  to  only  a 


274  MAGNETISM    IN    IRON. 

very  limited  extent ;  by  far  the  greater  number  of  the  lines 
through  P  will  complete  their  circuit  within  the  substance  of 
the  ring,  and  the  flux  at  Q  will  be  only  a  very  little  less  than 
the  flux  at  P.  We  may,  therefore,  in  such  a  case,  as  a  first 
approximation,  treat  the  flux  in  the  ring  as  constant,  and  apply 

the  equation  of  the  perfect  magnetic  circuit,  flux  = ^- , 

to  find  it.  This  quantity  is,  in  fact,  slightly  less  than  the  flux 
in  the  part  P,  because  the  resistance  of  the  actual  magnetic 
circuit  is  a  trifle  less  than  that  of  the  ring,  through  the 
"  shunting  "  of  a  part  of  the  ring  by  the  surrounding  air.  On 
the  other  hand,  the  flux,  as  calculated  above,  is  greater  than 
the  true  flux  at  Q. 

The  case  is  analogous  to  that  of  a  conducting  circuit,  which 
instead  of  being  perfectly  insulated  is  immersed  in  a  poorly 
conducting  fluid.  Imagine  a  ring  of  copper  with  a  seat  of 
electromotive  force  at  P  to  be  immersed  in  a  liquid,  the  con- 
ductivity of  which  is  only  one  two-thousandth  or  one  three- 
thousandth  of  the  conductivity  of  copper.  The  current  at  Q  will 
be  only  a  little  less  than  the  current  at  P;  the  current  which 
leaks  into  the  surrounding  fluid  will  be  an  inconsiderable  part 
of  the  whole.  We  must  repeat  the  proviso  that  the  ring  is  short; 
in  other  words,  that  the  surface  through  which  leakage  occurs 
is  not  very  great  in  comparison  with  the  area  of  cross  section 
through  which  what  we  may  call  legitimate  conduction  occurs. 

The  advantage  of  regarding  the  iron  ring  as  a  magnetic  circuit, 
nearly,  though  not  quite,  perfect,  is  at  once  apparent  when  one 
considers  how  difficult  it  would  be  to  determine  directly  the 
magnetic  force  H  at  individual  points.  In  the  case  of  a 
uniformly  wound  ring  there  is  no  difficulty  in  determining  H, 
because  the  magnetic  force  is  then  wholly  due  to  the  mag- 
netising coil.  In  the  present  case  H  is  by  no  means  due  to  the 
coil  only.  The  coil  acting  alone  would  produce  a  strong 
magnetic  force  at  points  within  and  close  to  it,  and  would 
produce  very  little  magnetic  force  in  more  distant  portions  of 
the  ring.  But  we  know  that  H  must  actually  be  pretty  nearly 
uniform  throughout  the  ring,  because  the  magnetisation  is 
pretty  nearly  uniform.  What  tends  to  equalise  H  is  the  free 
magnetism  in  the  ring  itself — the  free  magnetism  which  exists  in 
consequence  of  the  very  fact  that  the  flux  is  not  quite  uniform. 


RING    WITH    A    GAP.  275 

The  magnetic  force  at  any  point  is  due  partly  to  the  action 
of  the  free  magnetism  and  partly  to  the  action  of  the  coil;  at 
points  within  and  near  the  coil  the  free  magnetism  diminishes 
H  by  opposing  the  action  of  the  coil,  but  at  points  on  the 
bare  side  of  the  ring  augments  H.  It  is  just  because  the  ring 
is  not  a  perfect  magnetic  circuit — because  there  is  some  leakage 
of  the  flux  into  surrounding  space — that  the  magnetic  force 
(and,  therefore,  the  induction)  is  fairly  uniform  all  round.  In 
a  short  ring  of  very  permeable  substance,  a  slight  variation  in 
the  flux  from  point  to  point  of  the  ring  implies  the  existence  of 
enough  free  magnetism  to  correct  very  nearly  that  excessive 
inequality  in  the  magnetic  force  which  is  produced  by  the 
magnetising  coil ;  in  other  words,  the  circuit  then  establishes 
itself  with  but  little  leakage. 

§  156.  Ring  Magnet  with  an  Air  Gap. — We  shall  next  con- 
sider a  magnetic  circuit  consisting  of  a  uniform  iron  ring,  in 
which  a  narrow  radial  crevasse  has  been  cut.  When  the  ring  is 
magnetised  there  is  some  leakage  of  lines  of  induction  through 
its  sides  into  surrounding  space,  especially  near  the  crevasse, 
but  most  of  the  lines  go  directly  across  the  crevasse.  We 
may  conceive  the  magnetic  circuit  of  the  ring  to  be  completed 
— though  not  quite  perfectly — by  a  plate  of  air  filling  the 
crevasse,  of  the  same  area  of  cross-section  as  the  ring 
itself.  The  lines  of  induction  spread  somewhat  in  crossing  the 
crevasse,  and  a  closer  approximation  to  the  condition  of  a  per- 
fect circuit  would,  therefore,  be  reached  by  supposing  the  plate 
of  air  to  have  an  area  of  cross-section  rather  larger  than  the 
cross-section  of  the  ring,  the  extent  of  this  enlargement  being 
dependent  on  the  thickness  of  the  crevasse.  In  the  case  which 
we  postulate,  however,  the  crevasse  is  very  narrow,  and  it  will 
suffice  to  take  its  area  of  section  as  no  more  than  equal  to  that 
of  the  ring.  Let  s  be  the  area  of  section,  I  the  mean  length  of 
the  complete  ring  (before  the  crevasse  is  cut),  and  8 1  the  (small) 
mean  thickness  of  the  crevasse.  Let  the  ring  be  magnetised, 
as  before,  by  a  coil  of  N  turns,  carrying  a  current  C.  The  per- 
meability of  the  ring  is  p,  and  that  of  the  gap  is  unity.  Then, 

Flux  =  magnetomotive  force    _  . —  ^  4  IT  C  N  p  s 

magnetic  resistance     ~  ~ —  +  —  =  I  +  8 1  (u.  -  1)" 
/*«          * 

T2 


276  MAGNETISM   IN   IRON. 

If  there  had  been  no  gap,  the  flux  would  have  been  -    ^  8. 

The  effect  of  removing  a  short  length,  8  I,  of  the  iron,  and  sub- 
stituting air  as  the  material  through  which  the  magnetic  circuit 
is  completed,  is  to  increase  the  resistance  of  the  circuit  as  much 
as  it  would  be  increased  by  the  addition  of  a  length  of  iron 
equal  to  8  1  (/A-  1). 

§  157.  Comparison  of  a  Split-Ring  with  an  Ellipsoid.  —  It  is 

interesting  to  compare  the  case  of  a  ring  in  which  there  is  a 
gap  with  that  of  an  ellipsoid  of  finite  length.*  In  the  ellip- 
soid, as  we  have  already  seen  (§  26),  the  free  magnetism  pro- 
duces a  self-demagnetising  force,  which  is  proportional  to  the 
amount  of  magnetisation,  and  opposes  the  action  of  the  mag- 
netising coil.  If  we  call  H  the  true  magnetising  force  acting 
on  the  metal,  and  H'  that  part  of  the  magnetising  force  which 
is  due  to  the  action  of  the  coil  alone,  then 

H  =  H'-^I, 

where  I  is  the  intensity  of  magnetisation,  and  N  is  a  numerical 
factor,  the  value  of  which  depends  on  the  relation  of  the  length 
of  the  ellipsoid  to  its  transverse  dimensions.  We  shall  see  that 
a  precisely  similar  formula  may  be  obtained  for  the  ring  with  a 
gap  by  treating  it  as  a  nearly  perfect  magnetic  circuit. 

Since  the  magnetisation  of  the  cut  ring  is  very  nearly 
uniform,  the  actual  magnetic  force  in  the  iron,  which  is  the 
resultant  of  that  due  to  the  coil  and  that  due  to  the  free  mag- 
netism, must  also  be  very  nearly  uniform.  Call  this  force  H, 
and  call  H'  the  magnetising  force  due  to  the  coil  alone,  which 

(on  the  supposition  that  the  coil  is  uniformly  wound)  is  -  « 
The  H-B-Flux-  47TCN/.S  4  ?rCN 

' 


u,        7r 
and  H  = 

9 


Therefore,  H'  I  =  H  {I  +  S I  (jt  -  I)}, 
H-.HJ  1+^0-1) 


See  a  Paper  by  H.  E,  J.  Q.  du  Bois,  Phil.  Mag.,  Vol.  XXX.,  1890,  p.  335. 


SELF-DEMAGNETISING   FORCE   DUE    TO    GAP. 


277 


since  JK  =  4  TT  K  + 1,  K  being  the  magnetic  " susceptibility," or 


Hence, 


I 
H' 


and 


The  factor  ^       *  therefore  takes  the  place  of  the  factor  N 
L 

in  the  formula  for  ellipsoids.  Its  magnitude  depends  on  the 
proportion  of  the  width  of  the  crevasse  to  the  whole  length  of 
the  circuit. 

Taking  the  case  of  a  circular  ring,  this  proportion  may  be 
expressed  by  reference  to  the  angular  aperture  of  the  crevasse 
— that  is  to  say,  the  angle  subtended  by  the  crevasse  at  the 

£  7  A 

centre.    Calling  this  angle  a  in  degrees,  —  =  -— -  and  JV  =  — — . 

I      360  «360 

The  following  table  has  been  calculated  by  Du  Bois,  to  show 
what  aperture  of  crevasse  in  a  circular  ring  produces  the  same 
self-demagnetising  force  as  exists  in  ellipsoids  of  certain  stated 
elongations : — 


Ratio  of  Length  to  Diameter 
of  Ellipsoid. 

Factor 
N. 

Equivalent  Aperture  in 
Circular  Ring  (degrees). 

20 
30 
40 
50 
100 

0-0848 
0-0432 
0-0266 
0-0181 
0-0054 

2-41 
1-22 
0-76 
0-52 
0-15 

It  is  scarcely  necessary  to  add  that  the  self-demagnetising 
force  which  is  introduced  by  the  presence  of  the  crevasse  affects 
the  residual  magnetism  of  the  ring  as  well  as  the  induced 
magnetism,  precisely  as  it  does  in  the  ellipsoid.  When  the 
magnetising-circuit  of  the  split-ring  is  broken,  the  residual 
magnetism  causes  a  reversed  force  to  act  on  the  metal,  the 


value  of  which  is 


|r,  where  lr  is  the  residual  intensity  of 


magnetism.       This    prevents    the    residual    magnetism    from 
being  nearly  so  great  as  it  would  be  were  the  ring  complete — 


278  MAGNETISM  IN  IRON. 

indeed,  a  very  narrow  crevasse  is  sufficient  almost  wholly  to 
destroy  the  (otherwise  very  great)  residual  magnetism  of  a  soft 
iron  ring.  For  example,  in  a  ring  of  soft  annealed  iron,  which, 
when  uncut,  would  retain,  after  being  strongly  magnetised,  a 
residual  induction,  Br,  of  12,000  units,  the  presence  of  a  gap 
only  half  a  degree  wide  will  reduce  the  residual  value  of  the 
induction  to  about  1,000. 

§  158.  Graphic  Representation  of  the  Influence  of  a  Narrow 
(Jap. — The  influence  of  a  narrow  gap,  both  in  resisting  mag- 
netisation and  in  promoting  demagnetisation,  is  best  seen  by 
resorting  to  the  graphic  construction  which  has  been  already 
explained  in  relation  to  ellipsoids  and  long  rods  (§  48).  Let 
a,  a,  a  (Fig.  132)  be  curves  of  magnetisation  (curves  of  I  and 
H)  for  the  iron  of  which  the  ring  is  composed.  Find  the 

A         £  / 

factor   N,  equal    to  ,   and  draw  the   line  0  A,  so  that 

i 

A  M  (drawn  parallel  to  the  axis  along  which  H  is  measured, 
and  interpreted  on  the  scale  of  H)  shall  be  to  0  M  as  — — — . 

(/ 

is  to  I.  Then  the  intercepts  between  0  M  and  0  A  represent 
the  values  of  the  self-demagnetising  force,  due  to  the  corre- 
sponding values  of  I,  and  if  we  wish  to  represent  the  relation 
of  the  magnetism  to  the  magnetising  force  produced  by  the 
coil  alone  (the  force  which  has  been  called  H'  above),  we 
have  only  to  draw  a  diagram  in  which  the  lines  a,  a,  a  are 
sheared  into  the  position  b,  b,  b  by  taking  the  abscissas  from 

A         £  7    I 

0  A  instead  of  from  0  M,  or,  in  other  words,  by  adding  — — 

to  H  in  every  case.  Thus,  any  point  F  in  the  new  curve 
is  found  from  the  corresponding  point  P  by  taking 
P'  R  =  P  R  +  Q  R.  The  residual  magnetism,  which  was  0  S  in 
the  ring  without  a  gap,  is  reduced  to  0  S'  in  the  ring  with 
a  gap.  If  the  object  of  the  construction  had  merely  been 
to  find  the  residual  magnetism,  0  S',  that  could  have  been 
done  more  readily  by  drawing  0  T  inclined  at  the  same 
angle  as  0  A,  but  on  the  other  side  of  the  axis  of  I,  to  meet 
the  descending  curve  a,  and  projecting  S'  from  the  point  of 
intersection  of  0  T  with  the  curve.  The  same  construction 
will,  of  course,  serve  to  find  the  residual  magnetism  of  ellipsoids, 


GRAPHIC   TREATMENT   OF   RING   WITH   GAP. 


279 


or  of  long  rods,  which  may  be  treated   as  approximating  to 
ellipsoids.* 

In  Fig.  132  we  have  supposed  that  the  magnetisation  of  the 
iron  is  exhibited  by  means  of  a  curve  of  I  and  H.  If,  instead 
of  this,  the  curve  of  B  and  H  were  given,  a  similar  graphic 
construction  would  still  serve  to  show  the  effect  of  the  gap. 

Since  I  =  B~H,  the  self  demagnetising  force  N\  =  N  (B  ~  H), 


which,  in  a  very  permeable  substance  like  iron,  is  practically 


FIG.  132. 


NB 


equal  to  ,  since  B  is  very  great  compared  with  H.     Sub- 

4  7T 

stituting  for  N  its  value  4  v  8 1,   this    becomes    ?A?.      The 

L  t, 

line  0  A  has,  therefore,  to  be  drawn,  in  a  diagram  of  B  and  H,  at 

D  <>  -I 

such  an  inclination  that  when  0  M  represents  B,  M  A  is 

B  -  H 

From  the  equation  H  =  H'  -  N  \,  by  substituting for  I, 


we  have 
or 


H-H'-L'(B-H), 

L 

H'/:=  HC-80  +  B8J. 


*  This  construction,  for  finding  the  residual  magnetism  of  ellipsoids,  is 
given  by  J.  Hopkinson,  Phil.  Trans.,  1885,  p.  465. 


280  MAGNETISM   IN    IRON. 

H'  I  is  4  TT  C  N;  it  is  the  line-integral  of  the  magnetic  force  taken 
round  the  whole  circuit,  or,  in  other  words,  the  magnetomotive 
force.  H  is  the  magnetic  force  in  the  iron,  and  H  (I  -  8 1)  is  that 
part  of  the  line-integral  which  is  taken  through  metal.  B  is 
equal  to  the  magnetic  force  in  the  gap,  and  therefore  B  8 I  is  that 
part  of  the  line-integral  that  is  taken  through  air.  The  equation 
might  evidently  have  been  written  down  directly ;  it  expresses 
the  simple  fact  that  the  line  integral  for  the  complete  circuit 
is  made  up  of  two  parts,  in  one  of  which — namely,  the  iron, 
whose  length  is  I  -  8 1 — the  magnetic  force  has  the  sensibly 
uniform  value  H,  while  in  the  other — namely,  the  gap  whoso 
length  is  81 — the  magnetic  force  has  the  sensibly  uniform 
value  B.  We  have  derived  it  otherwise,  in  order  to  accustom 
the  student  to  observe  the  connection  between  the  treatment 
of  the  ring  as  a  magnetic  circuit  and  that  other  treatment 
which  deals  with  the  magnetic  condition  at  individual  points. 
In  the  language  of  the  magnetic  circuit,  H  (1  —  81)  represents 
that  part  of  the  whole  magnetomotive  force  which  is  used 
in  overcoming  the  magnetic  resistance  of  the  iron,  and  B  8 1 
represents  the  remainder  of  the  magnetomotive  force,  which  is 
used  in  overcoming  the  resistance  of  the  gap.  In  soft  iron,  if 
the  gap  is  of  any  considerable  width,  its  resistance  is  so  great 
compared  with  that  of  the  iron  that  nearly  the  whole  magneto- 
motive force  is  used  in  forcing  the  induction  across  the  gap. 

§  159.  Graphic  Representation  of  the  Relation  of  Flux  to 
Magnetomotive  Force. — In  dealing  with  the  magnetic  circuit 
as  a  whole,  it  is  convenient  to  modify  and  generalise  the 
graphic  construction  exemplified  in  Fig.  132,  by  drawing  the 
abscissas  to  represent  the  whole  magnetomotive  force,  and  the 
ordinates  to  represent  the  whole  magnetic  flux  in  the  manner 
first  described  by  J.  and  E.  Hopkinson.*  Such  a  curve  may 
obviously  be  derived  for  any  part  of  a  magnetic  circuit  from 
the  curve  of  induction  and  magnetic  force  for  the  material 
by  multiplying  fche  induction  by  the  area  of  section  s  to 
find  the  whole  flux,  and  by  multiplying  the  magnetic  force  by 
ihe  length  of  the  piece  to  find  the  magnetomotive  force  re- 
quired for  the  magnetisation  of  that  part  of  the  circuit.  Then, 

*  Phil.  Trans.,  1886,  Part  I.,  p.  331. 


GENERAL  GRAPHIC  METHOD. 


281 


by  graphically  summing  the  abscissas  for  successive  parts  of  any 
composite  magnetic  circuit,  the  whole  magnetomotive  force  is 
represented  in  relation  to  the  flux.  An  example  will  make  the 
method  intelligible.  Take,  as  before,  the  case  of  an  iron  ring 
of  uniform  section  with  a  gap  in  it,  the  length  of  the  gap  being 
8 1,  and  that  of  the  iron  1-81.  From  the  curve  of  B  and  H 
for  the  metal  of  which  the  ring  is  formed — which  we  suppose 
to  be  known — draw  the  curve  0  P  (Fig.  133),  for  the  iron,  in 
which  any  ordinate,  Pp,  is  the  flux,  B  s,  and  the  correspond- 
ing abscissa,  Op,  is  H  (1-8  I).  Next  draw  the  curve  0  Q 


P  q 

MAGNETOMOTIVE  FORCEi 
FIG.  133. 


for  the  gap,  in  which  the  ordinate  Q  q  is  again  B  s,  and  the 
corresponding  abscissa  0  q  is  the  magnetomotive  force  required 
for  that  part  of  the  circuit,  namely  B  8 1.  The  line  0  Q 
is  evidently  straight,  as  it  relates  to  a  non-magnetic  substance 
in  which  induction  is  proportional  to  magnetic  force.  Then 
draw  the  resultant  curve  0  R,  in  which  for  each  ordinate 
the  abscissa  is  the  sum  of  the  abscissas  of  the  curves  already 
drawn,  namely,  Or  =  0p  +  0q.  Or  is  the  magnetomotive 
force  required  for  iron  and  gap  together,  and  the  curve  0  K 
shows  the  relation  of  the  flux  to  the  magnetomotive  force  in 
the  circuit  as  a  whole. 


282  MAGNETISM    IN    IRON. 

Moreover,  the  construction  may  be  applied  with  equal 
facility  to  the  descending  limb  of  the  curve,  or  to  exhibit  the 
behaviour  of  the  circuit  in  any  cycle  of  magnetisation.  In  the 
line  0  R  the  descending  and  ascending  limbs  coincide  ;  in  the 
iron  part  of  the  circuit  the  ascending  and  descending  limbs 
have  to  be  drawn  separately,  and  the  process  of  summing  the 
abscissas  has  to  be  applied  successively  to  each  limb  (as  in  Fig. 
132)  in  order  to  determine  a  curve  which  will  show  the  effects  of 
hysteresis  in  the  magnetic  circuit  as  a  whole,  and  all  the  varia- 
tions of  magnetic  flux  under  cyclic  variations  of  magnetomotive 
force. 

Again,  the  method  may  evidently  be  extended  to  magnetic 
circuits  of  a  more  complicated  form,  containing,  let  us  say, 
successive  pieces  of  different  material,  of  lengths  lv  /2,  13,  &c., 
and  sections  sv  s2,  s3,  &c.  We  must  know,  to  begin  with,  the 
curve  of  B  and  H  for  each  material.  From  these  curves  draw 
a  set  of  curves  in  which  the  ordinates  are  respectively  B  slt 
B  s2>  B  s3,  &c.,  and  the  abscissas  are  Hj  llt  H2 1%>  H3  /3,  &c.  The 
required  curve  of  flux  and  magnetomotive  force  for  the  whole 
circuit  will  be  found  by  compounding  these  curves ;  that  is  to 
say,  by  drawing  a  curve  in  which,  for  a  given  ordinate,  the 
abscissa  is  the  sum  of  the  abscissas  of  the  separate  curves. 
The  complete  curve  exhibiting  what  happens  when  the  complex 
circuit  is  carried  through  a  cyclic  process  of  magnetisation  may 
be  found  in  this  way,  provided  the  cyclic  curves  for  each  of  the 
materials  are  determined  beforehand. 

§  160.  Application  to  Dynamos. — A  principal  use  of  this 
method  is  to  determine  the  magnetomotive  force,  and  conse- 
quently the  number  of  ampere-turns,  required  to  produce  a 
stated  magnetisation  in  a  circuit  made  up  of  pieces  the  dimen- 
sions and  magnetic  qualities  of  which  are  known.  The  method 
was,  in  fact,  invented  by  J.  and  E.  Hopkinson  as  a  means  of 
solving  practical  problems  in  the  design  of  a  dynamo,  where 
the  magnetic  circuit  is  made  up  of  (1)  the  cores  of  the  field 
magnets,  (2)  the  yoke,  (3)  the  pole  pieces,  (4)  the  core  of  the 
armature,  and  (5)  the  non-magnetic  spaces  on  either  side  of  the 
armature  core,  between  it  and  the  pole  pieces.  This  last  is  much 
the  most  important  item  in  the  resistance  of  the  circuit.  The 
magnetic  circuit  of  a  dynamo  is  far  from  perfect,  and  the 


APPLICATION   TO   DYNAMOS.  283 

estimation  of  the  effective  length  and  effective  cross-section  of 
each  part  is  subject  to  some  uncertainty,  so  that  the  results  are 
no  more  than  rather  roughly  approximate.  To  pursue  this 
application  in  detail  would  be  beside  our  present  purpose  :  the 
student  should  in  any  case  refer  to  the  original  Paper.*  One 
point,  however,  must  be  briefly  mentioned,  being  of  general 
interest  in  relation  to  other  magnetic  circuits  as  well  as  to  the 
circuit  of  the  dynamo. 

In  the  dynamo  circuit  the  flux  is  by  no  means  uniform 
throughout  ;  there  is  much  leakage.  The  flux  is  greatest  in  the 
magnet  limbs,  which  are  the  seat  of  the  magnetomotive  force, 
and  in  the  armature  it  is  considerably  less.  Its  value  in  the 
armature  is,  however,  the  matter  of  chief  interest  in  the  prac- 
tical problem.  Calling  Fx  the  value  of  the  flux  in  the 
armature,  the  fluxes  F2,  F3,  &c.,  in  other  parts  of  the  circuit 
may  be  expressed  by  the  use  of  factors  <?2,  g3,  &c.,  such  that 
F2  =  <£2  F-p  F3  =  q3  Fp  and  so  on.  These  factors  are  sometimes 
called  coefficients  of  leakage  ;  in  the  case  considered  they  are 
greater  than  unity.  They  may  be  found  experimentally  by  com- 
paring the  forces  ballistically  by  means  of  induction  coils  wound 
at  different  places  in  the  circuit,  or  by  measuring  directly  the 
number  of  stray  lines  of  induction  in  the  air  round  about  the 
several  portions.  They  are  not  strictly  constant,  but  tend  to 
increase  when  the  flux  approaches  saturation.  When  they  are 
known,  we  may  obtain  a  better  approximation  to  the  true 
equation  of  the  magnetic  circuit  by  writing 


H  S3 

or  4 


/V2 

§  161.  Bar  and  Yoke.  —  In  speaking  of  applications  of  the  idea 
of  the  magnetic  circuit,  we  may  revert  briefly  to  the  arrange- 
ment of  bar  and  yoke,  first  used  by  Hopkinson  in  experiments 
on  susceptibility,  and  described  above  in  §§  58-59,  Figs.  26  and 
27.  The  function  of  the  yoke  is  to  make  the  bar  form  part  of 

*  LOG.  cit:  see  also  a  Paper  by  E.  Hopkinson  on  the  "  General  Theory  of 
Dynamo  Machines,"  Rep.  Brit.  Assoc.,  1887,  p.  614.  Reference  should  also  be 
made  to  Prof.  S.  P.  Thompson's  "  Treatise  on  Dynamo-Electric  Machines." 


284  MAGNETISM   IN    IRON. 

a  nearly  perfect  magnetic  circuit,  of  which  the  resistance  of 
the  bar  itself  is  nearly  the  whole  resistance.  Let  ^  be  the 
effective  length  of  the  bar,  which  is  somewhat  greater  than  its 
clear  length  within  the  yoke  (since  there  is  a  gradual  spreading 
out  of  the  lines  of  induction  where  the  bar  penetrates  the  yoke), 
and  let  sl  be  the  cross-section  of  the  bar.  Let  Z2  be  the  length 
of  the  return  path  of  the  lines  through  the  yoke,  and  s2  the 
cross  section  of  the  return  path,  which  is  the  sum  of  the  cross 
sections  of  the  two  sides  of  the  yoke.  Let  N,  as  usual,  be  the 
number  of  turns  of  the  magnetising  coil,  which  is  wound  on  the 
bar.  Then,  by  the  principle  of  the  magnetic  circuit, 


where  Bx  is  the  magnetic  induction  within  the  bar.  The 
flux,  B!  sv  is  the  quantity  which  the  ballistic  test  measures. 
The  equation  may  be  written 


Now  H,  the  true  magnetic  force  acting  on  the  bar,  is  -1 ; 
hence  H  =  — 


The  magnetic  resistance  of  the  block  therefore  virtually  adds 
a  small  piece  to  the  length  of  the  rod  —  a  piece,  namely,  whose 

length  is  ^L?l  L,  and  the  effect  is  that  the  actual  magnetic  force 

/*2S2 

is  equal  to  the  force  due  to  the  magnetising  solenoid  _?!_  - 

*i 
minus  a  small  correction,  the  amount  of  which  may  be  written 

thus  : 


This  correction  may  be  made  insignificantly  small  by  using 
for  the  yoke  a  material  of  the  greatest  possible  permeability, 
and  giving  it  an  area  of  section  very  many  times  greater  than 
that  of  the  bar.* 

*  See  Hopkinson,  Phil.  Trans.,  1885,  p.  458. 


BAR   AND    YOKE.  285 

The  amount  of  the  correction  is  not  constant,  even  when  ex- 
pressed as  an  addition  to  the  length  of  the  bar,  for  /^  and  fjL2  are 
functions  of  the  magnetic  state  of  the  bar  and  yoke  respectively, 
and  bear  no  constant  proportion  to  each  other.  In  all  that  has 
been  written  regarding  the  magnetic  circuit,  fj.  has  simply  this 
meaning,  that  it  is  the  ratio  of  the  induction  which  happens  to 
exist  at  the  moment  to  the  magnetic  force  which  happens  to 
exist  at  the  moment.  The  value  of  the  correction  depends, 
therefore,  not  merely  on  the  magnetic  force  actually  in  opera- 
tion, but  on  the  previous  magnetisation  of  the  circuit.  The  cor- 
rection may,  of  course,  be  very  completely  made  by  the  graphic 
process  which  has  been  described,  provided  we  have  data  from 
which  to  draw  a  curve  of  B  and  H  for  the  material  of  the  yoke. 

We  have  spoken  of  this  magnetic  circuit  as  if  it  were  wholly 
made  up  of  the  bar  and  the  yoke.  In  fact,  however,  there  is 
another  constituent,  the  importance  of  which  will  be  more 
apparent  presently.  This  is  the  joint  at  each  end  of  the  bar ; 
between  the  bar  and  the  yoke.  We  shall  see  immediately  that 
a  joint,  that  is  to  say,  a  discontinuity  in  the  substance  of  the 
magnetic  circuit — even  when  there  is  no  perceptible  space 
separating  the  parts — interposes  some  resistance.  Its  effect  is 
equivalent  to  that  of  a  very  narrow  air-gap. 

Acting  like  an  air-gap,  each  joint  in  the  circuit  tends  to  shear 
over  the  curve  of  magnetisation,  and  one  effect  is  that  the 
residual  magnetism  of  the  circuit  is  reduced.  This  is  a  rather 
serious  objection  to  the  use  of  the  yoke  for  determining  the 
permeability  of  soft  iron. 

§  162.  Magnetic  Resistance  of  Joints. — The  fact  that  a  joint 
offers  magnetic  resistance  seems  to  have  been  first  noticed  by 
J.  J.  Thomson  and  H.  F.  Newall,  who  found  that  when  an  iron 
bar  was  cut  in  two,  and  the  pieces  were  put  in  contact,  the 
susceptibility  of  the  bar  was  considerably  reduced.* 

In  the  following  experiments!  a  tolerably  full  examination 
was  made  of  the  influence  of  a  joint  in  adding  magnetic  resist- 
ance to  an  iron  bar,  both  when  the  surfaces  of  the  joint  were 

*Proc.  Camb.  Phil.  Soc.,  1887. 

t  "  On  the  Influence  of  a  Plane  of  Transverse  Section  on  the  Magnetic 
Permeability  of  an  Iron  Bar  "  (by  the  writer  and  W.  Low). — Phil. 
Sept.,  1888. 


286 


MAGNETISM   IN   IRON. 


placed  in  simple  contact,  and  when  they  were  pressed  close  by 
externally  applied  force.  The  bar  was  a  turned  piece  of 
wrought  iron,  0*79  cm.  ha  diameter,  and  it  was  tested  by 
the  ballistic  method  within  a  yoke  which  allowed  a  clear 
length  of  12'7cms.  of  the  bar  to  be  exposed.  Over  the  whole 
of  this  length  a  magnetising  coil  was  uniformly  wound : 
the  magnetising  forces  which  will  be  stated  below  are  the 
forces  due  to  this  coil.  The  area  of  cross-section  which  the 
yoke  provided  for  the  return  of  lines  of  induction  outside 
the  bar  was  more  than  one  hundred  times  greater  than  the 
cross-section  of  the  bar ;  nearly  the  whole  magnetic  resist- 
ance of  the  circuit  was,  therefore,  that  of  the  bar  itself,  and 
of  the  joint,  or  joints,  in  it.  The  magnetisation  of  the  bar  was 
tested  by  observing  the  transient  current  induced  in  a  small 
secondary  coil,  wound  at  the  middle  of  the  length,  when  the 
current  in  the  magnetising  coil  was  reversed.  Successive  obser- 
vations were  made  in  this  way,  with  magnetising  currents  that 
were  progressively  increased,  to  determine  in  each  case  a  curve 
connecting  B  in  the  bar  with  the  magnetising  force  of  the  coil. 
The  bar  was  first  tested  without  any  cut,  and  then  when 
cut  in  the  middle  into  two  parts,  the  ends  of  which  were  care- 
fully scraped  to  form  true  planes  before  being  put  into  contact. 
The  truth  of  the  surfaces  which  formed  the  joint  was  tested 
by  comparison  with  a  Whitworth  surface-plate.  Notwith- 
standing the  closeness  of  contact  which  this  procedure  ensured, 
the  joint  was  found  to  offer  a  very  appreciable  amount  of 
resistance,  as  the  following  figures  will  show  : — 

Table  XXVI. — Influence    of  a   smooth  joint  in  reducing   the 
magnetic  induction  in  an  iron  bar. 


Magnetising 

Magnetic  Induction  B. 

force  due  to 
solenoid. 

Bar 

uncut. 

Bar  cut  in  two  pieces  with  surfaces  of 
the  joint  faced  to  be  true  planes. 

4 

3,950 

3,000 

6 

6,900 

5,300 

8 

9,250 

7,400 

10 

10,900 

9,150 

15 

13,250 

12,000 

20 

14,300 

13,500 

30 

15,200 

14,900 

MAGNETIC    RESISTANCE    OF   JOINTS.  287 

§  163.  Calculation  of  the  Equivalent  Air-gap.  —  The  in- 
fluence of  a  joint  in  adding  magnetic  resistance  may  be  con- 
veniently expressed  by  calculating  the  width  of  an  air-gap 
which  would  have  the  same  resistance,  assuming  the  permea- 
bility of  the  metal  itself  to  be  wholly  unaffected  by  cutting. 
The  width  of  the  equivalent  air-gap  is  readily  found  in  the 
following  way*  :  — 

Let  Hj'  be  the  magnetising  force  due  to  the  solenoid  when 
the  bar  is  uncut,  and  H2'  the  magnetising  force  due  to  the 
solenoid  when  the  bar  is  cut,  both  for  the  same  value  of  B. 
Let  I  be  the  length  of  the  bar,  and  s  its  area  of  cross-section. 
Let  x  be  the  width  of  the  air-gap  equivalent  in  magnetic 
resistance  to  the  joint.  Then,  by  the  principle  of  the  mag- 
netic circuit 


and  H2'Z  =  —  +  Bx. 

f* 

Since  B  is  the  same  in  both  cases,  //.  is  the  same.     Hence, 


and 


To  find  x,  we  have  therefore  to  draw  curves  of  B  and  H/  and  of 
B  and  H2',  and  measure  the  horizontal  distance  from  one  curve 
to  the  other,  that  is  to  say,  the  difference  of  H'  for  the  same 
value  of  B.  The  quantity  H/  I  is  the  magnetomotive  force 
that  suffices  to  produce  the  induction  B  when  the  bar  is  uncut. 
The  quantity  (H^-H/)/  is  the  additional  magnetomotive 
force  that  is  required  to  force  the  same  induction  B  through 
the  joint. 

In  Fig.  134:,  the  curves  are  drawn  for  the  experiment  which 
has  just  been  quoted,  and  the  values  of  H2'  -  H/  are  represented 
by  the  broken  line  at  the  side  of  the  figure.  This  line  is  not  far 

*  In  the  Paper  from  which  these  experiments  are  quoted  an  erroneous 
procedure  was  followed  in  calculating  the  width  of  the  equivalent  air-gap. 
The  error  had  the  effect  of  making  the  gap  appear  to  diminish  in  thick- 
ness as  the  magnetisation  was  strengthened.  The  figures  given  here  are 
corrected. 


288 


MAGNETISM    IN    IRON. 


from  straight — which  implies  that  the  width  of  the  equivalent 
air-gap  is  not  far  from  constant  throughout  the  range  of  values 
of  B  with  which  the  experiment  deals.  The  broken  curve 
does,  indeed,  incline  slightly  outwards  at  the  higher  values  of  B, 
implying  a  greater  width  of  equivalent  air-gap  in  the  region  of 
strong  magnetisation ;  but  it  may  be  questioned  whether  this 
slight  deviation  from  straightness  may  not  be  due  to  errors  of 
observation.  A  very  slight  error  in  the  value  of  B  in  one  or 
other  of  the  two  curves  would  suffice  to  account  for  it ;  and  in 
another  precisely  similar  experiment,  made  with  another  bar, 
the  line  showing  values  of  H2'-H1/  actually  bends  slightly 


leooo 


QQ 


;  1 2000 


8000 


4000 


<£ 


8  12  16  20  24 

MAGNETISING   FORCE    DUE   TO    SOLENOID    H    • 


28 


FIG.  134. — Influence  of  a  Smooth  Joint  on  the  Magnetic  Resistance  of  an 

Iron  Bar. 

inwards  at  high  values  of  B.  It  appears,  then,  that  the  joint  is 
equivalent,  in  magnetic  resistance,  to  a  narrow  gap  of  air,  the 
width  of  which  is  at  least  not  far  from  constant.  The  following 
are  the  widths  of  this  gap  calculated  for  the  experiment  of 
Table  XXVI.  and  Fig.  134. 

Width  of  equivalent  air- 
B.  gap  in  centimetres. 

4,000      0-0026 

6,000      0-0030 

8,000      0-0031 

10,000     0-0031 

12,000 0-0035 

14,000     0-0037 


WIDTH   OF   EQUIVALENT   GAP.  289 

The  corresponding  quantities  in  another  and  quite  indepen- 
dent experiment,  made  with  a  different  iron  bar,  were  : — 

Width  of  equivalent 
B.  air-gap  in  centimetres. 

6,000     0-0043 

8,000     0-0041 

10,000      0-0036 

12,000     0-0030 

In  this  case,  as  in  the  other,  the  ends  of  the  bar  after 
being  cut  were  carefully  brought  to  the  condition  of  true 
planes. 

We  may  take  a  width  of  0'0033cms.  to  represent  fairly  the 
equivalent  gap  in  the  first  case,  and  0'0036cms.  in  the 
second.  These  figures  agree  with  one  another  as  well  as  the 
circumstances  of  the  measurement  would  lead  one  to  expect. 
The  equivalent  gap  is  not  very  wide,  but  it  is  difficult  to 
believe  that  the  surfaces  of  the  metal  were  actually  separated 
by  even  this  narrow  space.  It  seems  more  probable  that  the 
magnetic  resistance  of  the  joint  is  due  in  part  to  a  diminished 
permeability  in  the  metal  itself  at  and  close  to  each  surface, 
and  this  conjecture  receives  some  support,  as  may  appear  later, 
from  the  theory  which  ascribes  the  process  of  magnetisation  to 
the  rearrangement  of  molecular  groups. 

§164.  Influence  of  Compression  on  the  Magnetic  Resist- 
ance of  a  Joint. — Other  experiments  in  the  same  series*  were 
directed  to  examine  how  the  magnetic  resistance  of  a  joint  is 
affected  when  the  surfaces  are  pressed  into  close  contact.  The 
method  of  the  yoke  was  still  employed ;  the  yoke  was  placed 
so  that  the  bar  stood  vertically,  and  compression  was  applied 
to  the  bar  by  means  of  a  weighted  lever  at  the  top,  and  a  stop 
at  the  bottom,  as  in  Fig.  97,  §  122.  In  experiments  of  this 
kind  it  is,  of  course,  necessary  to  remember  that  the  permea- 
bility of  the  metal  itself  is  changed  by  compressive  stress  ;  the 
influence  of  the  joint  is  to  be  tested  by  comparing  the  resistance 
of  the  cut  bar  under  pressure  with  the  resistance  of  the  uncut 
bar  under  equal  pressure.  It  was  found  that  the  effect  of  pres- 
sure is  to  lessen  the  magnetic  resistance  of  the  joint,  so  much  so, 
indeed,  that  when  the  surfaces  composing  the  joint  are  true  planes, 

*PhU.  Mag.,  September,  1888,  p.  278. 


290 


MAGNETISM    IN    IRON. 


a  tolerably  strong  compressive  stress  almost  wholly  destroys  the 
resistance  of  the  joint,  and  restores  the  divided  bar  all  but  per- 
fectly to  the  magnetic  condition  of  an  uncut  bar.  This  effect 
vas  produced  almost  completely  by  a  stress  the  intensity  of 
which  was  226  kilogrammes  per  square  centimetre.  Under  this 
load  a  curve  of  B  and  H'  taken  with  the  cut  bar  was  practically 
indistinguishable  from  the  curve  taken  with  the  solid  bar. 
Smaller  loads  only  reduced  the  resistance  of  the  joint  without 
making  it  disappear,  and  a  progressive  reduction  of  the  resist- 
ance could  be  traced  as  the  loads  were  increased.  The  follow- 
Vg  table  gives  the  values  of  B  which  were  observed  in  an 
iron  bar,  first  when  solid  and  then  when  cut  in  two  parts 
with  faced  ends,  under  various  stresses,  the  magnetising  force 
due  to  thf  solenoid  being  brought  to  the  same  value  (5  C.-G.-S. 
units)  in  each  case.  This  magnetising  force  was  applied  after 
each  load  had  been  put  on. 

,/able  XXVII. — Influence  of  compressive  stress  in  reducing  the 
magnetic  resistance  of  a  joint. 


Jtress  in  kilos,  per  sq.  cm. 

Magnetic  Induction  B,  produced  in  each  case 
by  a  magnetising  force  in  the  coil  (H') 
of  5  C.-G.-S.  units. 

Before  Cutting. 

After  Cutting. 

0 

56-5 
113 
169-5 
226 

5,600 
5,400 
4,700 
4,050 
3,650 

4,700 
4,670 
4,200 
3,800 
3,650 

Here,  under  the  highest  stress,  the  disappearance  of  the 
joint's  resistance  was  complete  for  a  magnetising  force  of  5 
C.-G.-S.,  but  under  stronger  magnetising  forces  it  was  hardly 
so  perfect. 

In  connection  with  these  results  it  may  be  noted  that  the 

(Q2\ 
—  1,    amounting,   as    it    does,   to    less 

than  1  kilogramme  per  sq.  cm.,  when  B  is  5,000,  is  insig- 
nificant in  comparison  with  the  stress  produced  by  external 
loading. 


RESISTANCE    OF    HOUGH   JOINTS. 


291 


§  165.  Experiments  with  Rough  Joints. — Others  of  the  ex- 
periments dealt  with  bars  which  were  simply  cut  in  the  lathe, 
without  having  the  cut  ends  afterwards  scraped  to  the  form  of 
true  planes.  Joints  of  this  kind,  which  may  by  comparison  be 
called  rough,  were  found  to  offer  rather  more,  but  not  very  much 
more,  resistance  than  a  carefully  faced  joint,  so  long  as  the  cut 
bar  was  tested  without  compression.  But  under  compression 
the  difference  between  a  rough  and  a  smooth  joint  became  very 
manifest ;  the  resistance  of  the  rough  joint  was  comparatively 
little  reduced,  and  altogether  refused  to  disappear  even  under 
the  most  intense  stress. 

Table  XXVIII.  shows  the  effect  of  successive  cuttings  in 
an  iron  bar,  the  joints  being  in  every  case  of  this  comparatively 
rough  kind.  The  bar  was  tested  first  in  the  uncut  state,  then 
when  cut  in  two  parts,  then  in  four  parts,  and  finally  in  eight 
parts,  the  ends  being  put  in  contact  without  compression. 

Table  XX VIII. — Effect  of  Successive  Cuttings. 


Magnetising 

Magnetic  Induction  B. 

to  solenoid. 

Solid  bar. 

Bar  cut  in 
two. 

Bar  cut  in 
four. 

Bar  cut  in 
eight. 

7'5 

8,500 

6,900 

4,800 

2,600 

10 

11,000 

9,000 

6,400 

3,770 

15 

13,400 

11,550 

8,900 

5,550 

20 

14,400 

13,000 

10,750 

7,150 

30 

15,350 

14,550 

12,940 

9,800 

50 

16,400 

15,950 

15,000 

13,300 

70 

17,100 

16,840 

16,120 

15,220 

The  results  of  this  experiment  are  also  exhibited  in  Fig.  135, 
where  the  full  lines  show  the  relation  of  B  to  the  magnetising 
force  of  the  solenoid  when  the  bar  was  in  one,  two,  four  and 
eight  pieces.  The  dotted  lines  in  the  same  figures  refer  to  a 
further  experiment,  in  which  a  compressive  stress  of  226  kilos, 
per  square  cm.  was  applied,  first  to  the  uncut  bar,  and  then 
to  the  bar  cut  in  eight  pieces. 

Comparing  the  curves  for  the  uncut  bar  with  and  without 
compression,  we  see  that  compressive  stress  lowers  the  per- 
meability, except  when  the  magnetisation  is  strong.  In  strong 
fields  the  dotted  curve  crosses  above  the  plain  curve.  This  gives 


292 


MAGNETISM   IN   IRON. 


incidental  evidence  of  the  existence  of  a  reversal  of  the  effect  of 
compressive  stress,  corresponding  to  the  "  Villari"  reversal  of  the 
effect  of  the  tensile  stress  (see  §§  120,  124-126)— a  result  to  be 
anticipated  from  what  we  know  of  the  behaviour  of  iron  under 
tension.  For  values  of  B  below  16,000,  however,  compression 


16000 


14000 


•.12000 


GO 


10000 


6000 


6000 


4000 


£000 


IO  .20  130  40  60-60  7O 

MAGNETISING   FORCE    DUE  TO   SOLENOID     H  • 

Fia.  135. — Effects  of  Successive  Cuttings  on  the  Magnetic  Permeability  of 
a  Wrought  Iron  Bar. 

No  load 

Load  of  226  kilogs.  per  sq.  centim.    ; 


increases  the  resistance  of  the  circuit  so  long  as  the  bar  is 
uncut.  But  when  applied  to  the  eight  pieces,  compression 
decidedly  reduces  the  resistance  of  the  circuit,  even  when  the 
magnetisation  is  weak :  the  dotted  curve  for  the  bar  cut  in 
eight  lies  considerably  above  the  plane  curve.  In  other 


WIDTH   OP   EQUIVALENT   GAJ». 

words,  compression  lowers,  though  it  by  no  means  destroys,  the 
resistance  of  the  joints,  and  when  the  joints  are  as  numerous 
as  they  are  here,  its  favourable  effect  on  them  more  than 
counteracts  its  detrimental  effect  on  the  permeability  of  the 
metal  itself.  When  the  same 'test  was  applied  to  the  bar  in  four 
pieces  it  was  found  that  the  two  effects  of  compression  came 
near  to  neutralising  each  other. 

In  the  following  table  the  width  of  the  air-gap  which  would 
give  the  same  resistance  as  the  mean  of  the  seven  joints 
(introduced  by  cutting  the  bar  into  eight  pieces)  has  been  cal- 
culated by  the  method  described  above.  The  results  are 
stated  for  both  cases — with  compression  and  without  com- 
pression. 

Table   XXIX. —  Width    of  air-gap   equivalent   in  resistance  to 
the  mean  of  seven  joints. 


B. 

Without  compression. 

With  compression  of  226 
kilos,  per  sq.  cm. 

8,000 
10,000 
12,000 
14,000 
15,000 

cms. 
0-0036 
0-0041 
0-0046 
0-0050 
0-0052 

cms. 
0-0024 
0-0031 
0-0036 
0-0041 
0-0041 

It  appears  then  that,  in  round  numbers,  the  resistance  of 
each  rough  joint  wras  nearly  the  same  as  that  of  a  film  of  air 
0 -005cm.  thick  when  there  was  no  compression,  and  that  this 
equivalent  film  was  only  reduced  to  about  0 '004cm.  when  a  com- 
pressive  stress  was  applied  which  would  have  been  intense  enough 
to  practically  destroy  the  resistance  of  the  joint  had  the  surfaces 
been  carefully  faced.  We  have  seen  that  a  joint  with  faced 
surfaces,  tested  without  compression,  is  equivalent  to  a  film  of 
air  about  0 -003cm.  thick.  The  thickness  of  the  equivalent  film 
in  these  rough  joints  seems  to  increase  a  little  as  the  condition 
of  saturation  is  approached.  In  the  absence  of  compression  a 
smooth  joint  is  not  very  greatly  better  than  a  rough  one. 
But  compression  is  incompetent  to  produce,  in  a  rough  joint, 
that  extreme  closeness  of  contact  which  it  apparently  produces 
in  a  smooth  joint,  in  consequence  of  which  the  resistance  of  the 
smooth  joint  almost  vanishes. 


CHAPTEE  XL 


MOLECULAR   THEORY. 

§  166.  Molecular  Theories :  Poisson  and  Weber.— We  know 
that  when  a  piece  of  iron,  or  other  magnetic  metal,  is  mag 
netised,  the  magnetic  state  permeates  the  whole  piece.  A  steel 
bar  magnet  may  be  broken  up  into  small  pieces,  and  every 
piece  is  found  to  exhibit  magnetic  polarity.  Assuming  the 
structure  to  be  molecular,  it  is  inferred  that  each  molecule  of 
the  magnetised  bar  is  a  magnet.  Taking  a  row  of  molecules  in 
the  direction  of  the  magnetisation,  we  have  the  north  pole  of 
one  contiguous  to  the  south  pole  of  the  next,  and  so  on  along 
the  row — with  the  result  that  it  is  only  at  the  ends  of  the  row 
that  free  poles  appear.  Imagine  the  row  to  be  broken  into 
two  or  more  parts,  however,  and  each  segment  of  it  has  free 
poles  at  its  ends. 

The  individual  molecules  of  a  magnetised  bar,  then,  are 
magnets,  and  the  question  next  arises  whether  they  become 
magnets  only  when  the  bar  is  magnetised.  Does  the  process 
of  magnetising  consist,  as  Poisson  suggested,  in  making  each 
molecule  become  a  magnet  ?  Or  are  we  to  adopt  Weber's  view, 
according  to  which  the  molecules  are  always  magnets,  showing 
no  aggregate  polarity  in  an  unmagnetised  piece,  only  because 
their  axes  point  in  all  directions  at  random,  but  turning  into  line 
when  a  magnetising  force  is  applied?  According  to  Poisson,  there 
is  no  need  to  suppose  the  molecules  capable  of  moving  within  the 
bar,  but  we  must  suppose  that  magnetic  polarity  can  be  induced 
in  the  individual  molecules.  In  other  words,  the  question  how 
induction  happens  is  only  shifted  from  the  bar  to  the  molecule, 
and  is  brought  no  nearer  to  a  solution.  According  to  Weber, 
on  the  other  hand,  the  molecules  are  to  be  conceived  as  free,  more 


WEBER'S  THEORY.  295 

or  less,  to  turn  and  take  up  a  new  alignment,  very  much  as  a 
pivoted  compass-needle  will  turn  when  it  is  directed  by  a  mag- 
netic field ;  but  there  is  no  need  to  imagine  any  development 
of  polarity  within  the  molecule  itself.  The  Weber  molecule  is 
a  magnet  before  the  force  begins  to  act,  and  the  amount  of 
magnetism  in  it  need  suffer  no  change  however  widely  the  mag- 
netism of  the  bar  be  altered.  Hence  Weber's  theory  explains 
the  process  of  induction  to  this  extent,  that  it  makes  the  mag- 
netic change  of  the  bar  be  brought  about  by  a  change  in  the 
position  of  the  molecules,  and  not  by  any  change  in  the  quality 
of  the  molecules  :  the  magnetising  process  simply  consists  in 
turning  the  molecules  to  face  one  way.  Of  the  two  views, 
Weber's  is  the  one  that  consorts  best  with  our  general  under- 
standing of  the  characteristics  of  molecules.  Moreover,  it 
receives  strong  support  from  certain  of  the  known  facts  of 
magnetic  induction. 

§  167.  Experimental  Evidence  in  favour  of  Weber's  Theory 
from  the  facts  of  Saturation,  &c. — It  would  be  difficult,  in 
Poisson's  theory,  to  give  any  reason  for  the  manner  in  which 
the  magnetisation  of  a  magnetic  metal  tends  toward  a  limit  as 
the  magnetising  force  is  increased.  If  the  process  consists  in 
the  development  of  magnetic  polarity  in  the  individual 
molecules  there  is  no  obvious  reason  why  it  should  not 
admit  of  being  extended  without  limit,  nor  why  the 
relation  between  the  magnetism  of  a  bar  and  the  magneti- 
sing force  should  have  the  exceedingly  complex  character  it  is 
known  to  possess.  We  should  rather  expect  to  find  propor- 
tionality, or  something  like  proportionality,  between  magnetism 
and  magnetising  force,  and  we  should  not  expect  to  find  residual 
magnetism  or  other  phenomena  of  hysteresis.  Weber's  theory 
on  the  other  hand,  implies  that  there  must  be  a  limit  to  the> 
intensity  of  magnetisation.  The  limit  is  reached  when  all  the 
molecules  have  become  turned  to  face  exactly  in  the  direction 
of  the  applied  magnetising  force ;  no  increase  of  the  force 
beyond  what  is  required  for  that  can  add  to  the  magnetisation. 
The  fact  that  a  definite  saturation  value  is  now  known  to  exist* 
adds  much  probability  to  Weber's  hypothesis.  Further,  the 

*  The  evidence  of  this  has  been  fully  stated  above  (§§  91  to  107). 


296  MAGNETISM   IN   IRON. 

process  by  which  the  molecules  are  supposed  to  turn  hither 
and  thither  under  varying  magnetising  forces,  leaves  ample 
room,  as  we  shall  presently  see,  for  a  satisfactory  explanation 
of  all  the  features  which  the  curves  of  magnetisation  are  known 
to  present,  and  the  various  manifestations  of  hysteresis  become 
intelligible.  Again,  the  effects  of  vibration  in  augmenting  mag- 
netic susceptibility  are  readily  accounted  for  in  consequence  of 
the  greater  freedom  which  vibration  gives  the  molecules  to  fall 
into  line  with  the  magnetising  force.  Additional  evidence  is 
furnished  by  experiments  such  as  that  of  Beetz*,  in  which  the 
effects  were  observed  of  applying  a  weak  magnetising  force  to 
iron  at  a  time  when  the  molecules  were  peculiarly  free  to 
respond  to  its  directive  action,  namely,  while  they  were  in  the 
act  of  being  deposited  by  the  electrolysis  of  an  iron  salt.  The 
iron  was  deposited  along  a  line  made  by  scribing  a  longitudinal 
scratch  on  a  straight  piece  of  varnished  silver  wire.  The  wire 
was  immersed  in  the  iron  salt,  and  was  placed  in  a  magnetic 
field  in  such  a  manner  that  the  lines  of  force  ran  in  the  direc- 
tion of  the  length.  The  silver  wire  formed  one  pole  of  an 
electrolytic  cell,  and  it  was  found  that  the  metal  deposited 
on  the  scratch  was  so  highly  magnetised  that  the  subsequent 
application  of  a  much  stronger  magnetic  field  failed  to  aug- 
ment its  magnetism  more  than  a  very  little.  The  molecules 
had  been  ranged  at  the  moment  when  they  escaped  from  im- 
prisonment in  the  salt,  and  before  they  had  the  opportunity 
of  forming  fresh  entanglements  by  their  action  on  one  ano- 
ther ;  just  as  criminals  are  said  to  be  most  easily  diverted 
into  regular  courses  at  the  moment  of  their  release  from 
gaol,  before  they  have  time  to  resume  the  ties  of  their 
usual  companionship.  Not  only  is  Weber's  notion  of  mole- 
cular magnets  strongly  supported  by  this  experiment  of 
Beetz,  but  the  cumulative  evidence  in  its  favour  which  is 
supplied  by  many  facts  of  more  recent  observation  may  be  said 
to  give  it  almost  conclusive  proof.  We  may  even  build  up  a 
model  consisting  of  small  permanent  magnets,  such  as  Weber's 
theory  postulates,  in  which  all  the  chief  characteristics  of  mag- 
netic induction  can  be  closely  imitated.  The  study  of  a  model 
of  this  kind  leaves  little  room  for  doubt  that  the  basis  of 

*  Pogg.  Ann.,  CXI,  1860,  p.  107. 


CONSTRAINT   OP    THE   MOLECULAR    MAGNETS.  297 

Weber's  theory,  namely,  the  hypothesis  of  permanently  mag- 
netic molecules,  is  essentially  sound. 

§168.  Constraint  of  the  Molecular  Magnets  in  Weber's 
Theory. — It  is  clear  that  if  the  process  of  magnetic  induction  is 
to  be  explained  as  the  turning  of  molecular  magnets  so  that 
they  tend  to  face  one  way,  the  molecules  must  be  subject  to 
some  directive  force  which  prevents  them  from  responding  with 
perfect  freedom  to  the  magnetising  field.  Without  some  such 
constraint  they  would  at  once  take  the  direction  of  the  applied 
field,  and  the  weakest  magnetising  force  would  suffice  to  pro- 
duce saturation.  In  fact,  however,  magnetisation  goes  on  pro- 
gressively as  the  magnetising  force  is  increased,  and  at  every 
stage  the  direction  taken  by  each  molecule  is  determined  by  a 
balance  between  the  force  of  the  field  which  tends  to  turn 
the  molecule,  and  some  other  controlling  force  which  opposes 
the  turning. 

Weber  supposed  that  in  a  piece  of  virgin  iron  the  axes  of  the 
molecular  magnets  point  indifferently  in  all  directions,  and  that 
when  a  magnetising  force  H  is  applied,  each  molecule  is 
deflected  against  a  directive  force,  which  tends  to  restore  it  to 
its  original  position.  He  assumes  this  force  to  be  that  which 
would  be  exerted  by  a  magnetic  force  of  some  constant  value, 
K,  acting  in  the  primitive  direction  of  the  molecule's  axis*.  The 
direction  in  which  the  molecule  points  while  the  magnetising 
force  acts  is  consequently  the  direction  of  the  resultant  of  H  and 
K,  and  when  the  external  force  H  is  removed,  the  molecule  is 
brought  back  by  K  to  its  primitive  position.  This  theory  of 
the  constraint  of  the  molecules  gives  no  explanation  of  residual 
magnetism  or  other  manifestations  of  hysteresis.  According  to 
it,  the  magnetic  susceptibility  should  be  constant  for  all  values 
of  H  less  than  K,  and  should  diminish  for  higher  values  of  H. 
At  the  stage  when  H  becomes  equal  to  K,  and  the  proportion- 
ality of  magnetisation  to  magnetising  force  ceases,  the  value  of 
I  should  be  §  of  the  final  or  saturation  value.  This  hypothesis 
is  inconsistent  with  the  fact  that  the  early  part  of  the  curve  of 
magnetisation  is  not  straight ;  that  the  susceptibility  is  small 

*  Fogg.  Ann.,  LXXXVIL,  1852,  p.  167.  See  Maxwell's  El.  and  Mag.t 
Vol.  II.,  §  443. 


298  MAGNETISM   IN   IRON. 

at  first,  and  increases  with  increasing  magnetising  force.  This, 
indeed,  is  an  example  of  hysteresis,  and  for  the  phenomena  of 
hysteresis  the  theory,  in  this  form,  affords  no  room. 

§  169.  Maxwell's  Modification  of  Weber's  Hypothesis.— To 
remedy  this  defect  Maxwell  suggested  a  further  assumption 
based  on  the  analogy  of  magnetisation  to  mechanical  strain, 
with  the  object  of  admitting  conditions  under  which  the  position 
of  equilibrium  of  the  molecular  magnets  may  be  permanently 
altered.  He  supposes  that  when  a  molecule  is  deflected  by 
a  magnetising  force  H  it  returns  completely  to  its  primitive 
position  on  the  removal  of  H  provided  the  deflection  has  been 
less  than  a  certain  value,  but  returns  only  partially  if  the 
deflection  has  exceeded  that  value.  In  the  latter  case  its  axis, 
when  H  is  removed,  remains  turned  through  an  angle  which 
may  be  called  the  permanent  set  of  the  molecule.  Maxwell  has 
examined  the  consequence  of  this  supposition  at  some  length, 
assuming  the  molecules  in  a  given  piece  to  be  all  capable  of  the 
same  or  nearly  the  same  amount  of  elastic  deflection,  and 
assuming  a  constant  or  nearly  constant  controlling  force,  K,  to 
act  on  each  in  the  primitive  direction  of  its  axis.  This  hypothesis 
accounts  for  the  existence  of  residual  magnetism,  and  for  some 
of  the  phenomena  of  hysteresis ;  it  fails,  however,  to  explain  why 
hysteresis  should  be  found  when,  after  the  first  application,  a 
magnetising  force  is  removed  and  reapplied,  and  its  postulates 
about  controlling  force  and  the  condition  of  permanent  set  are 
arbitrary.  We  shall  see  presently  that  by  considering  the 
action  of  the  molecular  magnets  upon  one  another  conclusions 
are  reached  which  really  embody  Maxwell's  idea  of  elastic  and 
non-elastic  deflection,  though  the  controlling  force  and  the 
amount  of  elastic  deflection  are  no  longer  arbitrary  and  no 
lorger  the  same  or  nearly  the  same  for  all  the  molecules. 

§  170.  Hypothesis  of  Frictional  Resistance  to  the  Deflection 
of  the  Molecules. — The  suggestion  has  been  made  by  Wiede- 
mann  and  others  that  the  deflection  of  Weber's  molecular 
magnets  is  opposed  by  a  species  of  frictional  resistance,  which 
not  only  resists  the  magnetisation,  but  accounts  for  residual 
magnetism  and  the  effects  of  hysteresis  by  tending  to  hold  the 
molecules  from  returning  after  they  have  been  disturbed.  A 


CONSTRAINT  DUE  TO  MUTUAL  FORCES.         299 

directive  force,  such  as  that  postulated  by  Weber,  is,  of  course, 
still  necessary.  Several  of  the  observed  phenomena  might  be 
adduced  as  supporting  this  notion  ;  in  particular,  it  harmonises 
well  with  the  effects  which  are  known  to  be  produced  by  vibra- 
tion and  other  mechanical  disturbance  in  augmenting  magnetic 
susceptibility,  and  in  reducing  residual  magnetism;  and  also 
with  the  comparative  suddenness  with  which  the  resistance  to 
magnetisation  breaks  down  when  a  certain  stage  in  the  mag- 
netising process  is  reached.  But  if  the  molecules  were  held 
fast  by  friction  until  the  applied  force  became  sufficiently 
strong  to  start  them,  the  susceptibility  with  respect  to  very 
feeble  forces  should  be  zero,  whereas,  in  fact,  it  has  a  small  posi- 
tive and  initially  constant  value  (§§  86,  87).  To  make  the  notion 
of  frictional  control  agree  with  the  facts,  it  would  be  necessary 
to  assume  some  further  complication,  such  as  that  a  few  of  the 
molecules  in  any  given  piece  are  sensibly  free  from  friction,  and 
may  begin  to  turn  under  the  influence  of  the  weakest  forces. 

§  171.  The  Constraint  of  the  Molecules  due  to  their 
Mutual  Action  as  Magnets. — The  matter  becomes  immensely 
simplified  if  we  put  aside  all  these  arbitrary  postulates  re- 
garding controlling  force  and  resistance  to  turning,  and  inquire 
what  is  the  character  of  the  constraint  the  molecules  necessarily 
suffer  through  the  forces  which  they  exert  on  one  another  in 
consequence  of  the  fact  that  they  are  magnets.  It  has 
been  pointed  out  by  the  author*  that  this  restraint  is 
sufficient  to  account  for  the  observed  characteristics  of 
the  process  of  magnetisation,  that  it  completely  explains 
hysteresis,  and  that  it  at  least  offers  a  clue  to  those 
complicated  variations  of  magnetic  quality  which  are  known  to 
be  caused  by  the  variation  of  such  physical  conditions  as 
temperature  or  stress. 

In  proceeding  to  consider  the  equilibrium  of  the  molecules 
under  their  mutual  magnetic  forces,  it  is  clear  that  we  cannot 
confine  our  attention  to  any  one  molecule.  For  the  directive 
force  that  acts  on  any  one  molecule  depends  on  the  positions  of 
the  molecules  which  surround  it,  and  becomes  altered  when  these 
are  disturbed.  We  cannot  investigate  the  equilibrium  of  the 

*  See  "  Contributions  to  the  Molecular  Theory  of  Induced  Magnetism," 
Proc.  Roy.  Soc.,  Vol.  XLVIII.,  1890,  p.  342,  Phil.  Mag.,  Sept.,  1890. 


300 


MAGNETISM   IN   IRON. 


individual  without  including  in  the  question  the  equilibrium  of 
its  neighbours.  When  an  external  force  is  applied,  they,  as 
well  as  it,  are  deflected,  and  the  constraint  they  exercise  on  it 
suffers  change.  What  must  be  studied  is  the  configuration  of 
the  group  as  a  whole,  and  the  manner  in  which  the  group 
becomes  distorted,  broken  up,  and  rearranged  in  the  process  of 
applying  and  removing  an  external  magnetising  force. 

In  seeking  to  find  in  the  mutual  constraint  excited  by  the 
magnetic  molecules,  an  explanation  of  the  changes  of  suscepti- 
bility which  are  observed  as  a  magnetising  force  is  gradually 
applied  to  a  piece  of  iron  or  other  magnetic  metal,  it  should  be 
borne  in  mind  that  the  magnetising  process  may  be  broadly 
divided  into  three  stages  (as  was  remarked  in  §  141),  namely, 
the  stages  A,  B,  and  C  of  the  typical  curve  (Fig.  136). 


MAGNETIC  FORCE 

Via.  136. 


These  admit,  in  general,  of  being  distinguished  from  one 
another  without  difficulty,  though  the  passage  from  one  stage 
to  the  next  is  never  perfectly  abrupt.  In  some  cases,  however, 
it  is  remarkably  sharp,  as  in  the  curves  of  Figs.  120  and  121 
(pp.  230,  231),  which  relate  to  nickel  under  torsion,  and 
under  a  combination  of  torsion  with  longitudinal  pull. 

In  the  first  stage  the  susceptibility  is  small,  and  there  is 
almost  no  retentiveness.  In  the  second  stage  the  magnetism 
is  acquired  with  great  readiness,  and  much  of  it  may  be  retained 
if  the  force  be  removed.  In  the  third  stage  the  growth  of 
magnetism  is  again  slow,  and  what  is  acquired  in  it  does  not 
contribute  much  to  the  residual  magnetism.  We  shall  see  that 


STABILITY   OF    MOLECULAR   GROUPS.  301 

these  stages  are  just  such  as  the  molecular  theory  would  lead 
us  to  anticipate. 

§172.  Imaginary  Molecular  Groups.— A  Single  Pair. — By 
way  of  leading  up  to  the  consideration  of  groups  consisting  of 
many  magnetic  molecules,  we  may  begin  by  thinking  of  a 


FIG.  137. 

group  which  consists  of  a  single  pair.  Each  member  of  the 
pair  is  to  be  conceived  of  as  a  short  magnet  capable  of  free 
rotation  about  a  fixed  centre.  In  the  absence  of  all  external 
magnetic  force  this  pair  of  molecules  will  arrange  themselves  as 


FIG.  138. 


In  Fig.  137,  with  opposed  poles  exactly  in  the  line  joining  the 
centres.  Let  an  external  magnetic  force,  H,  now  be  applied  in 
any  direction  (Fig.  138). 

If  H  is  weak  the  molecules  will  be  but  slightly  deflected.   But 
as  H  is  gradually  increased  a  stage  will  be  reached  at  which 


302  MAGNETISM    IN    IRON. 

the  molecules  part  company,  and  fly  round  into  a  position 
in  which  the  direction  of  the  magnetic  axis  of  each  is  nearly 
parallel  to  H  (Fig.  139). 

Except  in  special  cases  perfect  parallelism  with  H  will  be 
reached  only  when  H  becomes  indefinitely  strong. 

Then  as  H  is  gradually  reduced  there  will  at  first  be  little 
change  in  the  configuration,  until  a  stage  is  reached  at  which 
a  sudden  return  to  the  condition  of  Fig.  138  occurs.  This  will 
happen  at  a  lower  value  of  H  than  that  which  was  needed  to 
break  up  the  group  of  Fig.  138;  here  we  have,  in  fact,  an 
elementary  example  of  hysteresis.  If  the  direction  of  H  is 
chosen  so  that  it  is  perpendicular  to  the  line  of  centres  this 
return  will  occur  only  when  H  is  reduced  to  zero.  In  the 
more  general  case,  illustrated  by  the  figures,  the  sudden  return 


FIG.  139. 

will  happen  when  H  has  a  small  finite  value,  and  then  the 
subsequent  reduction  of  H  to  zero  will  be  associated  with  a 
gradual  change  from  the  state  of  Fig.  138  to  that  of  Fig.  137. 
During  the  application  of  H  we  have  three  stages  ;  there  is, 
first,  the  slight  deflection  of  the  molecules  (Fig.  138)  which 
precedes  what  may  be  called  the  rupture  of  the  tie  that  holds 
them  in  line  with  one  another.  Then  there  is  the  sudden 
swinging  into  a  position  of  much  greater  deflection  when  that 
tie  is  broken.  Finally  there  is  the  continued  approach  towards 
perfect  alignment,  made  under  stronger  values  of  H.  During  each 
of  these  three  stages  the  group  is  acquiring  resultant  magnetic 
polarity  in  the  direction  of  H,  though  the  magnetisation  of 
the  individual  molecules  is,  by  assumption,  a  constant  quantity. 
In  the  first  stage  the  process  is,  so  to  speak,  perfectly  elastic— 


EQUILIBRIUM   OF   A   SINGLE   PAIR.  303 

that  is  to  say,  it  corresponds  to  the  elastic  stage  in  the  straining 
of  a  solid  when  there  is  no  permanent  set  left  after  the  removal 
of  the  straining  force.  If  we  suppose  H  to  be  removed  at  any 
part  of  the  first  stage,  the  molecules  at  once  return  to  their 
primitive  positions.  But  after  the  critical  value  of  H  has  been 
passed,  which  separates  the  first  stage  from  the  second,  this  is 
not  so ;  there  is  then  a  tendency  to  retain  the  new  configuration. 
We  shall  see  presently  that  this  tendency,  which  is  the  very 
essence  of  hysteresis,  becomes  much  more  conspicuous  when  we 
have  to  deal  with  larger  groups.  Finally  in  the  third  stage 
we  have  again  a  quasi-elastic  part  of  the  process  of  mag- 
netisation. 

To  begin  with,  the  equilibrium  of  the  group  is,  of  course, 
stable  with  respect  to  small  displacements.  Any  small  casual 
disturbance,  applied  and  removed,  will  leave  the  magnets 
swinging  about  the  position  of  equilibrium,  shown  in  Fig.  137. 
The  equilibrium  continues  to  be  stable  so  long  as  the  deflecting 
force  is  weak  (stage  A).  Bat  as  the  critical  point  is  approached, 
the  stability  becomes  reduced — just  at  the  end  of  stage  A  it  is 
neutral,  and  any  further  increase  of  H  brings  about  instability. 
The  molecules  then  precipitate  themselves  into  the  new  form 
(Fig.  139)  in  which  they  are  once  more  stable  so  long  as  H 
continues  to  act. 

To  express  the  matter  in  symbols,  let  us  suppose  that  each 
magnet  may  be  treated  as  a  pair  of  poles  of  strength  mt 
separated  by  a  distance  2  r,  which  is  the  length  of  the  magnetic 
axis.  Let  a  (Fig.  140)  be  the  angle  which  the  direction  of  the 
applied  deflecting  force  H  makes  with  the  line  of  centres  C  C', 
and  let  6  be  the  amount  of  deflection,  which  is  the  same  for 
both  magnets.  It  is  assumed,  in  the  first  place,  that  H  is  not 
so  strong  as  to  produce  instability. 

The  field  H  exerts  a  mechanical  force  m  H  on  each  pole,  or  a 
couple  on  each  magnet,  the  distance  between  the  parallel 
forces  of  the  couple  being  2  r  sin  (a  -  0). 

The  deflecting  moment  which  acts  on  each  magnet  is, 
therefore, 

2  H  m  r  sin  (a  -  0), 

and  this  is  to  be  balanced  by  what  we  may  call  the  restoring 
moment,  due  to  the  forces  which  the  magnets  exert  on  one 
another. 


304 


MAGNETISM   IN   IRON. 


These  forces  are  (1),  the  attraction  of  the  poles  P  Q ;  (2), 
the  attraction  of  the  poles  P'  Q' ;  (3),  the  repulsion  of  the 
poles  P'  Q  j  and  (4),  the  repulsion  of  the  poles  P  Q'.  Of  these 
forces  the  moments  of  the  third  and  fourth  balance  one  another, 
and  the  moment  of  the  second  is  insignificantly  small  compared 
with  that  of  the  first,  provided  the  distance  C  C'  is  not  much 
greater  than  the  length  of  one  magnet,  and  the  deflection  is 
not  great.  Under  these  conditions  it  will  suffice  to  consider 
the  restoring  moment  as  due  to  the  first  force  only,  namely,  to 


140. 
mutual  attraction  of  P  and  Q.     Its  value  is 

PQ*  ' 

C  N  being  the  perpendicular  distance  from  C  to  the  line  P  Q  ; 
and  the  condition  of  equilibrium  is  that 

P  Q2 *      *     *     *  V  /' 

As  0  is  increased  the  restoring  moment  at  first  increases,  but 
passes  a  maximum  at  a  value  of  6  which  depends  on  the  rela- 
tion of  the  length  r,  or  C  P,  to  the  length  C  C'. 


GROUPS   OP  PAIRS.  805 

When  H  and  0    are  sufficiently  increased  the  equilibrium 
becomes  neutral.     This  occurs  when 


£{ 


»"- 


From  these  two  equations  (1)  and  (2)  it  is  possible  to  deter- 
mine the  values  of  H  and  of  9  corresponding  to  the  critical 
point  in  the  deflection,  at  which  the  equilibrium  of  the  deflected 
molecules  becomes  neutral.  Any  greater  value  of  H  will  cause 
instability  ;  the  molecules  will  then  swing  violently  round  into 
a  new  position  of  equilibrium  with  their  axes  nearly  parallel  to 
the  direction  of  H. 

If  there  were  a  number  of  such  pairs  of  magnets,  of  the 
same  strength  and  the  same  pitch,  all  acted  on  by  the  same 
deflecting  field,  but  with  their  lines  of  centres  inclined  at 
various  angles  to  the  direction  of  H,  it  is  clear  that  some 
would  reach  instability  sooner  than  others,  as  H  was 
strengthened.  The  first  pairs  to  become  unstable  would  be 
those  which  were  inclined  at  something  more  than  a  right 
angle  to  H,  so  that  a  —  6  became  a  right  angle  when  the  value 
of  0  corresponding  to  instability  was  reached.  Other  pairs  would 
escape  passing  through  the  unstable  state  altogether,  namely, 
those  pairs  which  lay  initially  in  directions  nearly  parallel  to 
H.  How  nearly  parallel  to  H  they  must  lie  initially  in  order 
to  escape  instability  depends  on  the  extent  by  which  the 
distance  between  the  centres  exceeds  2  r. 

If  we  suppose  that  this  excess  of  distance,  or  clearance  be- 
tween the  poles,  as  one  may  call  it,  is  very  small,  then  the 
state  of  instability  in  pairs  which  lie  well  across  the  direction 
of  H  is  reached  approximately  when 


dB  PQ* 
which  happens  when  tan  <f>  =  —j^  $  being  the  inclination  of  the 

line  P  Q  to  the  line  of  centres  C  C'.  In  these  circumstances  the 
value  of  H  which  breaks  up  the  pair  is  i 

H_  m 

12  ^3  .  (a  -  r)2  sin  a  ;  •  v 


306  MAGNETISM   IN  IRON. 

where  a  stands  for  half  the  distance  between  the  centres  C  and  C'. 
This  does  not  apply  when  the  line  of  centres  is  nearly  parallel 
to  H.  In  the  special  case  when  the  line  of  centres  has  the 
same  direction  as  H,  but  the  magnets  point  initially  in  the 
direction  opposed  to  H,  there  is  no  stable  deflection  previous 
to  the  occurrence  of  instability.  The  critical  point  is  reached 
in  such  a  pair  when 

Hra 
=  - . 

The  general  behaviour  of  a  crowd  of  groups,  each  consisting 
of  two  magnets,  can  be  readily  enough  imagined,  and  still  more 
readily  examined  by  aid  of  a  model.  Until  the  first  of  the 
groups  breaks  up,  as  the  field  is  increased,  we  have  nothing 
but  quasi-elastic  deflection.  Then  the  groups  successively  reach 
the  critical  point,  so  that  a  rapid,  though  not  perfectly  sudden, 
development  of  resultant  polarity  on  the  part  of  the  crowd 
as  a  whole  is  observed.  Finally,  there  is  a  slight  further 
increase,  under  the  action  of  stronger  fields,  as  the  state  corres- 
ponding to  saturation  is  approached. 

Again,  as  the  field  is  gradually  reduced  many  of  the  groups 
will  return  to  their  initial  state.  Many  others,  however,  will 
assume  new  forms,  namely,  with  their  poles  pointing  just  the 
other  way  from  the  way  they  pointed  at  first,  and  the  effect  of 
these  will  be  to  contribute  a  resultant  residual  polarity  which 
persists  when  H  is  reduced  to  zero.  The  application  and 
removal  of  H  will  leave  a  majority  of  groups  pointing,  more  or 
less,  towards  the  direction  in  which  the  force  was  applied, 
although  at  first  there  was  no  preponderance  in  any  direc- 
tion. 

We  find,  therefore,  even  in  so  simple  a  grouping  of  magnetic 
molecules  as  this — namely,  a  grouping  in  isolated  pairs — many 
of  the  features  which  are  presented  in  the  magnetisation  of  iron. 
We  find  analogues  of  the  first,  the  second,  and  to  some  extent 
the  third  stages,  which  are  observed  in  curves  of  I  and  H,  and 
we  find  evidence  of  hysteresis  and  residual  magnetism.  But  a 
very  much  more  complete  reproduction  of  the  phenomena  of 
magnetisation  becomes  possible,  as  will  be  shown  presently,  if 
we  suppose  the  molecules  to  be  distributed  either  continuously 
or  in  groups  consisting  of  a  considerable  number  of  members. 


GROUPS  OP  FOUR  MAGNETS.  807 

The  behaviour  of  two-member  groups  would  agree  fairly  well 
with  what  is  known  to  happen  in  the  first  and  second  stages  of 
the  magnetising  process  in  iron.  It  seems,  however,  to  leave 
too  little  supplementary  magnetisation  to  be  acquired  during 
the  third  stage.  And  a  more  obvious  difficulty  is,  that  though 
two-member  groups  suffice  to  account  for  the  existence  of  some 
residual  magnetism,  they  fail  to  explain  the  high  retentiveness 
which  is  found  in,  say,  soft  iron,  where  we  often  find  more  than 
90  per  cent,  of  the  induced  magnetism  surviving  the  removal 
of  the  magnetising  force.  To  account  for  that,  something 
more  is  needed  than  the  constraint  exercised  by  each  member 
of  a  pair  on  the  other  member ;  the  molecules  must,  in  fact, 
form  new  ties  after  the  old  ones  have  been  ruptured,  and 


Fia.  141. 

to  allow  of  that  each  molecule  must  have  more  neighbours 
than  one. 

§  173.  Group  of  Four  Members. — A  better  approximation  to 
the  facts  will  be  obtained  if  we  deal  with  a  group  consisting 
of  four  little  magnets,  with  their  centres  at  the  four  corners  of 
a  square  (Fig.  141).  When  the  field  H  begins  to  act,  the 
members  of  the  group  are  all  slightly  deflected,  but  without 
at  first  becoming  unstable.  If  during  this  first  stage  the 
force  H  is  removed,  there  is  no  residual  displacement.  But 
when  H  is  sufficiently  increased  the  original  lines  of  the  group 
break,  and  the  members  tend  to  pair  themselves  anew  in 
lines  which  are  more  favourably  inclined  to  the  direction  of  H 
{Fig.  142).  Finally,  when  H  is  further  increased,  the  members 

x2 


308 


MAGNETISM   IN   IRON. 


of  the  group  are  gradually  ce»*npelled  to  take  the  position 
sketched  in  Fig.  143.  Next,  suppose  H  to  be  removed. 
There  will  be  a  return  from  the  condition  of  Fig.  143  to- 
that  of  Fig.  142,  but  the  pairing  shown  in  Fig.  142  will  be< 


FIQ.  142. 

maintained,  and  this  implies  a  large  amount  of  residual  mag- 
netisation. If  the  direction  of  H  be  then  reversed,  and  its  value 
gradually  increased,  a  stage  will  presently  be  reached  when  the- 
resultant  polarity  of  the  group  suffers  an  abrupt  change  through. 
the  reversal  of  the  lines  in  Fig.  142. 


FIG.  143. 


The  curve  of  magnetisation — that  is  to  say,  the  curve- 
showing  the  resultant  polarity  in  terms  of  H — for  the  single? 
group  of  four  members  is  sketched  in  Fig.  144. 


AGGREGATE   OP   GROUPS. 


309 


From  this  it  is  easy  to  see,  in  a  general  way,  what  would  be 
the  form  of  the  curve  for  an  aggregate  of  many  such  groups, 
variously  inclined  to  the  direction  of  H.  The  transition  from 
one  stage  to  another  will  be  gradual  in  the  aggregate,  for  it  will 
happen  at  different  values  of  H  in  different  groups.  Hence  the 
curve  will  assume  a  rounded  outline  in  place  of  the  sharp 
corners  of  Fig.  144. 

Moreover,  the  curve  obtained  during  the  removal  of  H  will 
not  coincide  with  that  obtained  during  the  application  of  H, 
except  the  process  be  stopped  at  a  very  early  point  in  the  first 


FIG.  144. 

Whenever  the  process  is' extended  far  enough  to  cause 
any  of  the  groups  to  reach  the  unstable  state  we  shall  find 
hysteresis.  The-  two  curves  will  not  coincide,  even  in  the  third 
stage.  Some  of  the  members  will  pass  through  an  unstable 
state  even  there.  After  the  first  re-arrangement  of  the,  group 
has  taken  place,  and  the  lines  have  become  directed  as  in  Fig. 
142,  there  may  be  a  second  breaking  up  and  passage  through  in- 
stability on  the  way  to  the  state  of  Fig.  143.  This  will  happen 
when  the  lines  of  centres  have  a  considerable  inclination  to  H, 
and  especially  when  the  poles  of  the  members  are  close  together. 
In  such  an  aggregate  of  groups  we  may  therefore  expect  to 


310 


MAGNETISM   IN   IRON. 


find  hysteresis  in  all  possible  cyclic  changes  of  the  magnetising 
force.  The  form  of  the  curve  obtained  during  reversal  of  H 
will  evidently  agree  with  the  general  form  given  by  the  mag- 
netic metals.  In  proportion  as  the  corner  between  stages  A  and 
B  in  the  first  curve  is  comparatively  sharp  or  comparatively 
rounded  so  will  be  the  corner  at  which  the  rapid  descent  of 
the  curve  begins  while  H  is  being  reversed. 


Fio.  145. 


§174.  Continuous  Distribution  in  Cubical  Order. — From 
these  considerations  regarding  groups  of  four  members  it  is- 
easy  to  pass  to  the  case  of  a  manifold  group  or  a  continuous 
distribution  of  members  arranged  so  that  the  lines  of  centres 
form  squares.  All  that  has  been  said  above  is  still  applicable. 
The  members  arrange  themselves  in  lines,  and  each  individual 
is  mainly  constrained  by  its  two  neighbours  in  the  same  line, 
instead  of  by  one  neighbour  as  in  the  case  already  spoken  of. 
The  equations  of  §  172  are  readily  adapted  to  members  of  »• 


GROUPS   OP  MANY   MEMBERS.  311 

long  row  by  substituting  2  m2  for  m2  in  the  expression  for  the 
restoring  moment.  The  three  stages  of  (1)  stable  deflection, 
(2)  instability,  with  rupture  of  the  original  lines  and  formation 
of  new  lines,  and  (3)  further  stable  deflection  are  as  readily 
traced  as  before,  as  will  be  evident  by  an  inspection  of  Figs. 
145,  146,  and  147. 

Fig.  145  represents  an  imaginary  primitive  arrangement. 
Fig.  146  is  the  configuration  reached  after  the  breaking  up  of 
the  primitive  lines,  and  Fig.  147  corresponds  to  saturation.  .,  •« 


FIG.  146. 

It  appears,  then,  that  the  theory  that  the  magnetic  molecules 
their  stability  to  the  magnetic  action  of  their  neighbours 
gives  results  which  agree  with  the  observed  facts,  whether  we 
conceive  the  molecular  structure  to  consist  of  isolated  groups, 
with  a  limited  number  of  members  in  each,  or  to  be  continuous. 
Even  with  a  continuous  distribution  the  lines  of  molecules 
will,  in  consequence  of  the  imperfect  homogeneity  of  the  piece, 
be  variously  inclined  at  various  places,  so  that  the  condition 


312  •*•       MAGNETISM   IN    IRON. 

necessary  to  give  a  rounded  outline  to  the  curve  will  in  any 
case  be  present.  In  -no  piece,  except  perhaps  in  a  single 
crystal,  could  we  expect  to  find  that  perfect  regularity  of 
structure  which  would  be  necessary  to  make  the  transition 
from  one  stage  of  the  magnetising  process  to  another  quite 
sudden,  and  to  give  the  curve  the  form  of  a  series  of  sharp 
steps. 

Whether  we  picture  the  structure  as  continuous  or  as  built 
up  of  isolated  groups,  special  importance  attaches  to  square 


FIG.  147. 

patterns  from  the  fact  that  the  magnetic  metals  crystallise  in 
the  cubic  system.  The  behaviour  of  pyramidal  forms  presents 
some  interesting  features  that  need  not  be  entered  into  here. 

Enough  has  already  been  said  to  show  that  there  is  no  need, 
to  assume  that  any  arbitrary  controlling  forces  act  on  Weber's 
molecular  magnets.  The  theory  that  their  constraint  proceeds 
only  from  their  mutual  action  as  magnets  evidently  suffices  to 
explain,  generally,  the  characteristics  of  the  magnetising  process 
It  may  be  useful,  however,  to  point  out  how  complete  is  the 


AGREEMENT   OF   THE   THEORY    WITH    FACTS.  313 

agreement,  in  point  of  detail,  between  the  deductions  which 
may  be  drawn  from  the  theory  and  the  facts  which  have  been 
described  in  earlier  chapters. 

§175.  Agreement  of  the  Theory  with  known  Facts  about 
Susceptibility. — In  the  first  stage  there  is  no  rupture  of 
molecular  ties  until  the  magnetising  force  is  sufficiently 
increased  to  bring  about  instability  in  the  least  stable  lines  or 
groups  of  molecules,  and  until  that  happens  the  application  and 
removal  of  the  force  has  no  residual  effect.  Up  to  that  point 
the  deflections  are  small,  and  they  are  initially  proportional  to 
the  applied  force.  All  this  is  in  complete  agreement  with  Lord 
Rayleigh's  experiments  on  the  susceptibility  of  iron  and  steel  to 
feeble  magnetising  forces  (§  87),  which  show  that  the  initial  value 
of  the  susceptibility  is  a  small  constant  quantity,  and  that 
residual  magnetism  begins  to  show  itself  only  when  the  mag- 
netising force  is  so  much  increased  that  the  proportionality  of 
magnetism  to  force  ceases.  Again,  it  accords  with  the  result 
that  a  small  alternating  change  of  H,  superposed  on  a  constant 
value  of  H,  or  acting  on  a  piece  which  has  residual  magnetism  in 
consequence  of  the  action  of  previous  forces,  produces  (after  the 
first  application)  but  a  small  coming  and  going  of  the  mole- 
cules without  breaking  their  ties,  and  that  if  this  small  alter- 
nating force  is  applied  when  the  magnetisation  is  already 
strong,  the  changes  which  it  causes  are  reduced  in  amount 
(§  87).  Again,  the  theory  might  lead  us  to  anticipate  the  fact 
that  if  at  any  point  of  the  ordinary '  magnetising  process  we 
stop  increasing  H  and  begin  to  decrease  it,1  or  stop  decreasing 
H  and  begin  to  increase  it,  the  initial 'rate  of  magnetic  change 

or  value  of  _— -  is  very  small,  depending,  as  it  does,  only  upon 
d  H 

the  quasi-elastic  movement  of  the  deflected  molecules.  Their 
movements  through  the  condition  of  instability  do  not  begin 
until  the  reversal  of  procedure  has  been  carried  some  little  way. 
Again,  in  strong  fields  the  behaviour  of  the  little  magnets 
accords  with  the  gradually  falling  off  in  susceptibility  which 
actually  occurs  in  magnetic  metals  as  the  state  of  saturation  is 
approached.  To  reach  the  state  of  perfect  saturation  would 
require  an  indefinitely  strong  directing  force,  but  the  alignment 
of  the  molecules  is  to  all  intents  complete  long  before  that.  In 


814  MAGNETISM   IN    IRON. 

view  of  the  molecular  theory  it  is  not  surprising  that  in  iron, 
where  many  molecular  groups  break  up  under  a  force  of  no 
more  than  two  or  three  C.-G.-S.  units,  a  force  of  two  or  three 
thousand  units  produces  (as  we  saw  in  §  102)  so  nearly  perfect 
saturation  that  augmenting  the  force  tenfold  adds  nothing 
perceptible  to  the  magnetisation. 

The  quantity  which  tends  to  a  limit  when  saturation  is 
approached,  is,  as  was  shown  in  §  93-102,  the  intensity  of  mag- 
netisation I,  not  the  induction  B.  According  to  the  molecular 
theory,  I  is  the  sum  per  unit  of  volume  of  the  moments  of 
the  molecular  magnets  resolved  in  the  direction  of  magnetisa- 
tion. If  n  be  the  number  of  molecular  magnets  in  unit  volume, 
and  m  the  moment  of  each,  the  saturation  value  of  I  is  m  n. 

§176.  Retentiveness  and  Residual  Magnetism. — An  equally 
satisfactory  agreement  is  found  when  the  results  of  experiments 
on  retentiveness  are  examined  in  the  light  of  the  molecular 
theory.  We  shall  take  advantage  of  the  opportunity  which  this 
discussion  of  the  theory  affords  to  describe  some  of  these  results 
more  fully  than  has  yet  been  done. 

In  the  first  stage  of  the  magnetising  process,  as  has  been 
already  remarked,  there  is  no  retentiveness  :  the  magnetism 
that  is  induced  under  very  weak  forces  disappears  entirely 
when  the  inducing  force  is  removed.  This  accords  with  the 
view  that  the  molecular  magnets  are  then  being  as  it  were 
elastically  displaced  from  a  position  of  stable  equilibrium, 
without  rupture  of  the  ties  by  which  the  initial  grouping 
maintains  itself,  so  that  each  molecule  simply  returns  to  itSc 
primitive  position  when  the  displacing  force  is  withdrawn. 
Theory  and  experiment  alike  show  that  this  condition  persists 
only  so  long  as  the  susceptibility  is  very  small. 

In  the  second  stage  the  susceptibility  has  become  much 
increased  as  a  consequence  of  the  large  deflection  the  molecular 
magnets  suffer  in  breaking  away  from  their  original  grouping  to 
form  new  combinations.  The  movements  they  then  accomplish 
are  in  great  measure  irreversible,  that  is  to  say,  they  are  not 
undone  as  the  magnetising  force  is  being  withdrawn.  We  may 
therefore  expect  to  find  a  rapid  development  of  residual  mag- 
netism during  that  part  of  the  magnetising  process  in  which  the 
susceptibility  is  high.  The  theory  shows  that  in  favourable 


RETENTIVENESS   AND    RESIDUAL   MAGNETISM.  315 

cases  nearly  the  whole  of  the  magnetism  acquired  during  that 
stage  will  persist  as  residual  magnetism.  Experimental  instances 
of  this  are  given  below. 

The  third  stage,  on  the  other  hand,  contributes  little  to  the 
residual  magnetism,  for  the  molecular  deflections  that  occur  in 
it  are  for  the  most  part  undone  as  the  magnetising  force  is 
withdrawn.  A  result  of  this  is  that  the  residual  magnetism 
approaches  saturation  sooner  (that  is,  under  the  action  of 
weaker  magnetising  forces)  than  does  the  induced  magnetism. 

Another  result  is  that  the  residual  magnetism  has  a  satura- 
tion value  which  is  definitely  less  than  the  saturation  value  of 
the  induced  magnetism.  It  is  indeed  possible  to  imagine  a 
molecular  structure  such  that  all  the  magnetism  of  saturation 
would  be  retained  on  the  withdrawal  of  the  force.  This  would 
be  the  case  in  a  cubical  formation  if  the  lines  of  centres  were 
parallel  and  perpendicular  to  the  direction  of  the  field  through- 
out the  whole  piece.  But  the  imperfect  homogeneity  of  any 
actual  piece  of  iron  puts  such  a  conception  out  of  court,  and 
when  any  of  the  lines  of  centres  are  inclined  to  the  field,  it  is 
clear  that  the  saturation  value  of  lr  is  less  than  that  of  I.  It 
will  be  shown  presently  that  a  continuous  cubical  formation 
with  lines  of  centres  uniformly  distributed  as  regards  inclina- 
tion is  a  structure  which  gives  more  than  sufficient  possibility 
of  residual  magnetism.  The  value  of  \r  which  the  theory  shows 
to  be  possible  in  such  a  structure  is  in  fact  greater  than  the 
values  which  are  found  in  experiments  with  even  the  most  re- 
tentive metal. 

The  molecular  theory  makes  it  easy  to  understand  the 
difference  between  retentiveness  and  what  may  be  called 
coercive  capacity,  by  which  is  meant  the  quality  that  the 
coercive  force  (§  47)  measures — the  quality  in  virtue  of  which  a 
substance  holds  its  residual  magnetism  so  strongly  that  a  con- 
siderable magnetic  force,  acting  in  the  reversed  direction,  is 
necessary  to  remove  it.  Retentiveness,  on  the  other  hand,  is  the 
quality  in  virtue  of  which  much  residual  magnetism  is  held, 
though  it  may  be  held  very  weakly.  Probably  no  magnetic  sub- 
stance has  so  much  retentiveness  as  soft  annealed  iron,  and  prob- 
ably none  has  so  little  coercive  capacity.  Eetentiveness,  by  the 
molecular  theory,  is  the  result  of  a  regular  molecular  structure 
of  such  a  kind  that  the  molecules  readily  arrange  themselves 


316 


MAGNETISM    IN    IRON. 


in  lines  which  are  but  little  inclined  to  the  direction  of  the 
applied  force.  The  molecular  ties  may,  however,  be  extremely 
weak.  Coercive  capacity  is  a  result  of  strong  ties,  such  as 
might  be  formed  by  reducing  the  distances  between  the  mole- 
cular centres  or  between  some  of  them,  and  this  condition  may 
very  well  exist  in  a  structure  where  the  lines  or  groups  are 
unfavourably  arranged  for  retentiveness. 

§  177.  Experiments  on  Residual  Magnetism  in  Iron. — The 
following  experimental  results*  were  obtained  with  straight 
iron  wires,  400  diameters  long,  using  the  direct  magneto- 
metric  method.  The  magnetising  force  was  gradually  raised 
to  an  assigned  value,  then  gradually  withdrawn,  to  allow  the 

Table  XXX. — Induced  and  Residual  Magnetism  in  a  Soft  Iron 
Wire,  Annealed  and  Hardened  by  Stretching. 


Before  stretching. 

After  stretching. 

H 

1 
induced. 

Ir 

residual. 

Ratio  of 
residual  to 
induced. 

H 

1 
induced. 

r 

residual. 

Ratio  of 
residual  to 
induced. 

0'42 

16 

3-9 

0-24 

0-42 

3-6 

0 

0 

0-58 

24 

6-6 

0"J7 

0-99 

13-1 

2-9 

0-22 

0'70 

33 

9-9 

0-30 

1-44 

21-1 

6-5 

0-31 

0-99 

62 

24 

0-40 

1-73 

26-9 

11-8 

0-38 

1-16 

91 

46 

0-50 

2*14 

41 

15-3 

0-38 

1-30 

140 

85 

0-61 

2-88 

72 

32-7 

0-46 

1-44 

195 

133 

0-68 

3-58 

116 

61-7 

0-53 

1-58 

280 

209 

074 

4-20 

167 

98 

0-59 

176 

364 

283 

078 

4-90 

218 

132 

0-61 

2-02 

468 

380 

C-81 

5-76 

265 

167 

0-63 

2-14 

507 

418 

0-S2 

7-20 

359 

225 

0-625 

2-28 

549 

455 

0-83 

10-78 

566 

327 

0-58 

2-51 

614 

513 

0-84 

11-90 

613 

348 

0-57 

274 

673 

568 

0-85 

15-20 

751 

381 

0-51 

2'88 

702 

598 

0-85 

17-50 

817 

399 

0-49 

3'16 

764 

650 

0-85 

23-61 

947 

414 

0-44 

3-58 

842 

711 

0-85 

29-81 

1017 

417 

0-41 

4-20 

926 

783 

0-85 

35-71 

1078 

419 

0-39 

5-02 

984 

832 

0-84 

41-90 

1114 

419 

0-38 

576 

1020 

848 

0-83 

6-46 

1050 

864 

0-82 

7'20 

1070 

877 

0-82 

8-64 

1110 

897 

0-81 

10-26 

1130 

910 

0-80 

11-91 

1150 

913 

0-80 

17-50 

1190 

929 

0-79 

23-61 

1195 

929 

0*78 

35*71 

1230 

933 

0-76 

45-51 

1230 

933 

0-76 

Ewing,  Phil.  Trans  ,  1885,  Part  II.,  pp.  556  et  seq. 


EXPERIMENTS    ON   RESIDUAL   MAGNETISM. 


317 


residual  magnetism  to  be  noted  ;  then  raised  to  a  slightly 
higher  value,  again  withdrawn,  and  so  on ;  so  that  the  values 
of  I  and  \r  were  ascertained,  corresponding  to  successive  steps 
in  the  magnetising  process.  The  results  will  be  seen  to  bear 
out  what  has  just  been  stated,  and  to  furnish  strong  evidence 
in  favour  of  the  theory  that  the  constraint  of  the  molecular 
magnets  is  due  to  their  mutual  magnetic  forces. 

Table  XXX.  gives  the  results  of  an  experiment*  in  which 
an  iron  wire,  l'58mm.  in  diameter,  was  tested,  first  in  the 
annealed  state,  and  then  after  being  hardened  by  stretching 
beyond  its  elastic  limit.  Inspection  of  the  figures  will  show 
that  the  ratio  of  residual  to  induced  magnetism,  which  is  at 
first  small  in  both  cases,  rises  to  a  maximum.  This  maximum, 


1200 


1000 


800 


600 


400 


300 


vV 

/  s 


Residua 


After 


tret 


Before  stretching. 


1  >efor e  stretching. 


Mi  gnet 


hint, 


Jf. 


O        4 


40      44      48 


12         16       20       34      28       32 

H 

Fio.  148. — Induced  and  Residual  Magnetism  in  Iron,  in  the  soft  state  and 
hardened  by  stretching. 

in  the  annealed  wire,  is  so  high  as  to  imply  that  the  rate  of 
increment  of  residual  magnetism  is  then  not  far  short  of  the 
rate  of  increment  of  induced  magnetism.  The  ratio  afterwards 
falls  off  as  the  magnetising  process  passes  into  its  third  stage. 

Fig.  148  is  drawn  to  exhibit  the  same  results.  It  shows 
well  how  the  residual  magnetism  approaches  its  maximum 
faster  than  the  induced  magnetism  does,  notably  in  the 
hardened  wire. 

This  mode  of  representing  the  results,  where  I  and  lr  are 
given  in  terms  of  H,  is  not,  however,  well  adapted  to  show 


Loc. 


.  559-60. 


318 


MAGNETISM    IN    IRON. 


what  is  the  saturation  limit  towards  which  \r  is  tending,  nor 
what  is  the  relative  rate  of  increment  of  the  two  at  various 
stages  of  the  magnetising  process.  To  bring  these  points  out 
we  may  draw  a  curve  showing  \r  in  relation  to  I  (Fig.  149). 
We  already  know  the  saturation  value  to  which  I  tends, 
namely,  about  1,700  C.-G.-S.  units  (§  98),  and  it  is  not  difficult 
by  extrapolation  of  the  curve  in  this  new  figure,  to  deduce  ai 
approximate  value  for  the  saturation  limit  of  lr. 

This  is  done  in  Fig.  149,  where  the  broken  lines  form  a  con- 
jectural extension  of  the  curves,  beyond  the  range  of  the  experi- 
ment, up  to  the  saturation  value  of  1,700  for  the  induced  I.  It 


1000 


800 


60° 


400 


200 


*     COO    4OO    600    800    1000    1200   J40O   1600   1800 

Induced  Magnetism  \ 

FIG.  149. — Proportion  of  Residual  to  Induced  Magnetism  in  Iron. 


appears  from  these  that  the  saturation  values  of  the  residual 
magnetism  in  this  specimen  are  approximately  970  when 
the  metal  is  annealed,  and  430  when  it  is  hardened  by 
stretching. 

An  inspection  of  the  curves  in  Fig.  149  will  also  show  that 
after  the  initial  stage  is  over,  in  which  the  residual  magnetism 
is  acquired  less  rapidly,  the  proportion  which  the  increment 
of  lr  bears  to  that  of  I  becomes  as  nearly  as  possible  constant, 
&nd  remains  so  (in  the  annealed  wire)  throughout  a  large 
part  of  the  whole  process  of  magnetisation.  From  the  point 
1  —  150,  or  so,  up  to  800  the  curve  is  practically  straight,  and 
•during  that  part  of  the  process  nearly  the  whole  of  the  mag- 


EXPERIMENTS   ON   RESIDUAL   MAGNETISM. 


319 


netism  that  is  acquired  goes  to  form  residual  magnetism.     By 
Table  XXX.  we  have 


H 

1 

Ir 

1-30 
3-16 

Difference  

140 
764 

624 

85 
650 

565 

So  that,  during  this  time,  |-f  £,  or  quite  92  per  cent,  of  the  magne- 
tism that  is  being  induced,  contributes  to  the  residual  magnetism. 

After  this  the  curve  bends  over  rather  quickly  and  — ^becomes 

d\ 

much  reduced.     In  other  specimens  of  annealed  iron  the  value 

of  —-£  during  the  steep  stage  was  even  more  nearly  unity. 
d\ 

This  was  the  case  in  the  experiment  of  Table  XXXI.,  made 
with  apiece  of  annealed  iron  wire  0'72mm.  in  diameter.*  In  this 
case  a  supplementary  experiment  was  made  to  determine  the 

Table  XXXI. — Induced  and  Residual  Magnetism  in  Annealed 
Iron  Wire,  with  and  without  Longitudinal  Pull. 


Load  =  0. 


Load  =  4  kilos.,  or  976  kilos,  per  sq.  mm. 


H 

1 
induced. 

Ir 

residual. 

Ratio  L 
Ir 

H 

induced. 

•T 

residual. 

Ratio  I 
•r 

0 

0 

0 



0 

0 

0 

_ 

1-08 

66 

32-5 

0-49 

0-54 

38 

21 

0-53 

1-62 

202 

141 

0'70 

1-08 

141 

94 

0-69 

2-16 

460 

381 

0-83 

1-62 

325 

242 

0-745 

270 

684 

601 

0-879 

2-16 

532 

419 

0-788 

3-24 

846 

767 

0-907 

2-70 

677 

543 

0-802 

378 

939 

860 

0-916 

3-24 

796 

640 

0-805 

4-32 

999 

920 

0-921 

3-78 

876 

705 

0-805 

5-40 

1071 

994 

0-928 

4-37 

937 

754 

0-804 

6-48 

1109 

1024 

0-923 

4'86 

978 

787 

0-805 

7-56 

1139 

1046 

0-919 

5-51 

1022 

816 

0-800 

8-64 

1157 

1063 

0-919 

6-48 

1067 

856 

0-800 

972 

1168 

1074 

0-919 

8-64 

1121 

891 

0-795 

10-8 

1178 

1032 

0-918 

10-8 

1162 

913 

0-786 

13-5 

1196 

1095 

0-916 

13-5 

1186 

926 

0-781 

16-2 

1210 

1105 

0-913 

16-2 

1204 

933 

0775 

18-9 

1219 

1111 

0-911 

18-9 

1211 

939 

0-775 

21-6 

1226 

1116 

0-910 

21-6 

1219 

942 

0-773 

25-6 

1236 

1119 

0-905 

26-2 

1232 

946 

0-768 

*  Loc.  cit.,p.  629. 


MAGNETISM    IN    IRON. 


influence  of  longitudinal  pull  on  the  residual  magnetism. 
After  the  test  made  in  the  ordinary  condition  of  no  load. 
a  steady  load  of  4  kilos,  or  9 '76  kilos,  per  sq.  mm.,  was  applied 
(a  load  well  within  the  elastic  limit),  and  the  observations 
in  the  second  portion  of  the  Table  were  made.  The  pro- 
portion of  \r  to  I  in  each  case  is  shown  in  Fig.  150,  where 
the  dotted  line  refers  to  the  experiment  in  which  wire  was 
in  a  state  of  longitudinal  tension.  The  full  curve  is  for  no 
load,  and  is  conjecturally  extended  to  find  the  saturation  value 
of  !„  which  is  higher  in  this  specimen  than  in  the  last,  namely, 
1210.  The  rate  of  increment  of  lr,  relatively  to  I  during  the 


1200 


1000 


800 


600 


400 


200 


r 


O      20Q    400    600    800    1000    1200    1400    1600    1800 

Induced  Magnetism  I. 

Fia.  150. — Proportion  of  Residual  to  Induced  Magnetism  in  Soft  Iron 
Wire,  loaded  and  without  Load. 

steep  part  of  the  curve  is  also  greater,  and  the  curve  is  prac- 
tically straight  throughout  a  wider  range.  The  following 
supplementary  Table  will  bring  this  out : — 


1 

V 

Differences  of  lr 
for  100  of  1. 

1 

w 

Differences  of  \f 
for  100  of  1. 

300 

232 

__ 

800 

722 

99 

400 

328 

96 

900 

822 

100 

500 

426 

98 

1,000 

921 

99 

600 

524 

98 

1,100 

1,020 

99 

700 

623 

99 

1,200 

1,100 

80 

EXPERIMENTS    ON    RESIDUAL    MAGNETISM. 


321 


It  appears  from  these  figures  that  in  the  stage  lying  between 
=  300  and  I  =  1,100,  or  so,  nearly  99  per  cent,  of  the  induction 
of  magnetism  was  taking  place  by  the  turning  round  of  the  mole- 
cules into  new  lines,  in  which  they  remained  when  the  magnetis- 
ing force  was  withdrawn.  Scarcely  any  of  the  induced  mag- 
netism was  then  being  contributed  by  quasi-elastic  deflections. 
After  1,100,  the  part  played  by  quasi-elastic  deflections  began 
to  be  considerable. 

In  the  test  made  while  the  wire  was  loaded  the  limit  to 
which  the  residual  magnetism  apparently  tended  was  about 
1020.  A  feature  to  be  remarked  is  that  in  the  earliest  stage 
the  curve  taken  with  load  lies  above  the  curve  taken  without 
load,  crossing  it  when  I  is  about  200.  The  presence  of 
longitudinal  pull,  though  unfavourable  to  the  retention  of 
magnetism  by  annealed  iron  when  the  magnetisation  is  strong, 
is  favourable  to  it  when  the  magnetisation  is  decidedly  weak 

Experiments  made  with  other  specimens  gave  results  which 
agreed  well  with  these.  With  another  piece  of  annealed  iron 
wire,  0'78mm.  in  diameter,  the  following  (amongst  other) 
readings  were  taken  : — * 


H 

1 

\r 

H 

i 

\r 

0-86 

26 

6 

5-40 

991 

898 

198 

164 

96 

6-81 

1,067 

946 

2-66 

478 

378 

11-20 

1,166 

1,014 

378 

806 

696 

17-24 

1,212 

1,042 

[n  this  case  between  H  =  2*66  and  H  =  6'81  the  increment  of 
I  is  589,  and  that  of  \r  is  568  or  96  per  cent,  of  the  other. 

One  more  experiment  of  the  same  class  may  be  referred  to 
in  further  illustration  of  the  influence  of  longitudinal  pull  on 
the  retentiveness  of  iron.f  In  this  instance  the  piece  tested, 
a  wire,  0'72m.  in  diameter  and  30'5cms.  long,  had  been 
hardened  by  stretching  beyond  its  limit  of  elasticity  before  the 
observations  were  made.  Its  retentiveness  was  then  examined 
when  without  load  and  also  when  various  amounts  of  steady 
pull  were  in  action.  The  curves  of  I,  also  of  lr,  each  in  rela- 

*  Loc.  cit.}  p.  559,  §  40.    Reference  to  the  same  Paper  should  be  made 
for  similar  experiments  with  steel  in  the  soft  and  hard  states. 
•\Loc.  cit.,  pp.  625-8,  §  110. 


322 


MAGNETISM   IN    IRON. 


tion  to  H,  have  already  been  given  in  Figs.  105  and  106 
(pp.  201-202)  respectively ;  but  the  points  to  which  attention  is 
now  directed  may  be  better  seen  by  reference  to  Fig.  151,  where 
curves  of  I  r  in  relation  to  I  are  drawn  for  no  load  and  for  two 
values  of  the  load.  These  show  that  a  moderate  amount  of  pull 
is  very  favourable  to  retentiveness  in  hardened  iron,  and  greatly 
augments  the  saturation  limit  towards  which  I,,  tends.  A 
stronger  pull,  on  the  other  hand,  is  less  favourable,  though 
under  the  greatest  pull  that  was  used  in  these  experiments  the 
wire  continued  to  be  more  retentive  than  it  was  in  the  unloaded 
state.  In  a  similar  experiment  made  with  steel  wire,  the 
amount  of  pull  was  further  increased,  and  was  then  found  to 


1000 


200         400 


1600        1800 


600          800        1000         1200        »400 

Induced  Magnetism  I 

Fia.  151.  —Proportion  of  Residual  to  Induced  Magnetism  in  Hard  Iron 
Wire,  loaded  and  without  Load. 

have  an  unfavourable  effect,  that  is  to  say,  it  reduced  the 
retentiveness  in  the  upper  part  of  the  process  below  the  value 
possessed  by  the  unloaded  wire. 

In  Fig.  151  the  apparent  saturation  limit  of  lr  is  about  460 
when  there  is  no  load,  and  this  is  raised  to  860  by  the 
presence  of  a  load  of  12-2  kilos,  per  square  mm.  It  is,  of 
course  very  possible  that  a  slightly  greater  or  slightly  less  load 
than  this  would  produce  a  still  more  favourable  effect  on 
the  saturation  value  of  the  residual  magnetism.  When  there 
is  no  load  the  rate  of  increment  of  lr  with  respect  to  I  at  the 
steepest  part  of  the  curve  is  about  0-7  ;  but  the  presence  of  a 
suitable  amount  of  load  raises  that  to  at  least  0-85. 


RETENTIVENESS    AND    THE    MOLECULAR    THEORY.  823 

§  178.  Retentiveness  of  Nickel. — A  reference  to  the  curves 
which  were  given  for  nickel  when  the  effects  of  stress 
were  discussed  in  Chapter  IX.  (§§  121-122,  Figs.  95,  96,  98, 
and  99,)  will  show  that  the  presence  of  longitudinal  push 
has  a  highly  favourable  effect  on  the  retentiveness  of  that 
metal,  and  on  the  maximum  of  residual  magnetisation.  Pull, 
on  the  other  hand,  is  extremely  unfavourable  to  the  retentive- 
ness  of  nickel.  A  comparison  of  the  results  set  forth  in 

Figs.  98  and  99  shows  that  the  value  of  — £,  which  is  at  no 

d\ 

stage  great  in  unstressed  nickel,  rises  to  a  maximum  approach- 
ing unity  when  the  metal  is  tested  under  the  influence  of  strong 
longitudinal  push.  And  it  is,  at  least,  highly  probable  that 
the  same  thing  occurs  at  the  steep  stage  of  the  magnetising 
process  in  the  tests  under  torsion  figured  in  Figs.  120  and 
121,  §141. 

§  179.  Amount  of  Retentiveness  possible  under  the  Mole- 
cular Theory. — The  full  bearing  of  these  experimental  results 
on  the  molecular  theory  is  not  easily  traced,  and  it  would  be 
scarcely  profitable  to  speculate  at  present  on  the  forms  in 
which  the  groups  of  molecular  magnets  may  conceivably  be 
arranged.  It  is,  however,  important  to  notice  that  the  theory 
leaves  ample  room  for  even  the  high  retentiveness  which  iron 
is  found  to  possess.  To  show  that  this  is  so  we  may  consider 
what  would  be  the  saturation  value  of  the  residual  magnetism 
if  the  structure  consisted  of  lines  like  those  of  Fig.  145,  with  the 
centres  of  the  molecules  grouped  in  cubical  order.  It  would 
be  unreasonable  to  postulate  any  particular  directional  relation 
between  the  lines  of  centres  and  the  direction  in  which  the 
piece  is  to  be  magnetised.  We  shall  suppose  that  the  structure 
is  an  aggregate  of  tribes  of  molecules,  with  a  cubical  formation 
for  each  tribe,  but  with  all  possible  variety  in  the  direction  of 
the  lines  of  centres.*  In  the  piece  as  a  whole  the  directions  of 
the  lines  of  centre  may  be  taken  as  uniformly  distributed ;  in 
other  words,  they  might  be  represented  by  all  possible  radii  of 

*  The  structure  may  be  continuous  ;  in  other  words,  the  transition  from 
one  direction  in  the  line  of  centres  (at  one  place  in  the  metal)  to  another 
direction  at  another  place  may  occur  through  very  slight  distortion  of  the 
cubical  formation. 


824  MAGNETISM   IN    IRON. 

a  sphere,  drawn  so  that  the  points  in  which  they  meet  the 
spherical  surface  are  equally  spaced. 

Suppose  that  a  very  strong  magnetising  force  H  is  applied, 
so  that  saturation  is  produced,  and  that  the  force  is  removed. 
We  have  to  consider  how  much  residual  magnetism  will  be  found 
when  the  molecules  have  returned  into  lines  in  which  they  are 
stable,  and  which  are  as  favourably  directed  for  giving  residual 
magnetism  as  the  assumed  structure  of  the  substance  will  permit. 

Let  a  be  the  angle  at  which  any  line  of  molecules  is  inclined  to 
the  direction  of  H,  before  the  process  of  magnetisation  begins. 
Since  the  distribution  of  direction  is  by  assumption  uniform, 
the  number  of  molecules  whose  inclinations  are  less  than  a  will 
be  to  the  whole  number  in  the  proportion  which  that  part  of 
a  spherical  surface  cut  off  by  a  cone  of  semi-angle  a  (with  its 
vertex  at  the  centre),  bears  to  the  whole  spherical  surface.  In 
the  same  way  the  number  of  molecules  whose  inclinations  lie 
between  c^  and  a2  will  be  proportional  to  the  area  of  that  belt 
of  the  sphere's  surface  which  is  cut  off  between  cones  with  ^ 
and  a2  for  semi-angle.  Let  the  whole  number  of  molecular 
magnets  per  unit  of  volume  be  n.  Then  the  number  whose 
inclinations  lie  between  a1  and  a2  will  be 

.(V 

-n  \       sm  a  a  a. 

J  ai 

Let  0  be  the  inclination  of  a  molecule  after  it  has  been  dis- 
placed by  the  application  and  removal  of  H.  If  m  is  the 
moment  of  a  single  molecule,  it  contributes  m  cos  9  to  the 
residual  magnetism.  The  whole  amount  of  residual  mag- 
netism contributed  by  those  molecules  whose  original  direction 
ranged  from  a2  to  alf  will  therefore  be 

mn 

sm  a  cos  6  d  a. 

And  to  find  the  whole  residual  magnetism  we  have  to  extend 
the  limits  of  this  integration  to  include  all  the  initial  direc- 
tions, from  a  =  0  to  a=  180  deg. 

We  have  next  to  consider  the  relation  of  0,  the  inclination 
after  H  has  been  applied  and  removed,  to  the  original  inclina- 
tion a.  Our  assumption  as  to  the  structure  makes  the  per- 


RESIDUAL    MAGNETISM    OP    SATURATION.  325 

ent   deflection  of    the   molecule    necessarily  either  0,   or 
deg.,  or  180  deg. 

(1)  Molecules  for  which  a  is  less  than  45  deg.  will  suffer  no 
permanent  deflection.     This  is  because  the  original  lines  are 
more  favourably  directed  than  lines  at  right  angles  to  them. 
For  these  molecules  0  =  a. 

(2)  Molecules  for  which  a  is  greater  than  45  deg.  and  less  than 
135  deg.  will  be  permanently  turned  through  one  right  angle. 
For  these  molecules  6  =  a  -  90  deg.,  and  cos  0  =  sin  a. 

(3)  Molecules  for  which  a  is  greater  than  135  deg.  will  be 
permanently  turned  through   two   right   angles.      For   these 
molecules  9  =  a  -  180  deg. 

The  whole  residual  magnetism,  therefore,  consists  of  the  sum 
of  three  terms,  namely 


_ 

mn  [4-  mn  [  * 

-s-j    smacosaacH--pr-  1     sm2a# 

A    J   Q  A     J   7T 


mn  f 
•~9~J       sinacos(a- 180°)c/a. 


4 

The  first  and  third  terms  are  of  equal  value.      The  integral  of 
the  first  term  is 

7T 

m  n  Fcos  2  a~~l4     mn     1 


The  integral  of  the  second  term  is 

m  n  Fa  -  sin  a  cos  a~"|  4  __  m  n  /TT     1  \ 

2  o ^~\I+9/ 

l_  I  "  *^         X -*•         ~*  s 

~4 

The  whole  residual  magnetism  is  therefore 


This  is  the  residual  magnetism  of  saturation,  and  is  to  be 
compared  with  the  induced  magnetism  of  saturation,  which  is 
mn. 

Assigning  to  m  n  the  value  1,700  this  calculation  shows  that 
a  continuous  structure  of  the  kind  postulated,  cubical  in 


826  MAGNETISM  IN 

arrangement,  is  competent,  on  the  molecular  theory,  to  have 
nearly  1,500  units  of  residual  magnetism,  an  amount  consider- 
ably greater  than  experiments  show  even  the  most  retentive 
iron  to  be  capable  of  holding.  It  is  clear,  therefore,  that  the 
intermolecular  magnetic  forces  are  abundantly  sufficient  to 
account  for  residual  magnetism,  and  that  the  actual  structure 
of  soft  iron,  and  still  more  that  of  hard  iron,  steel,  nickel, 
and  cobalt,  is  less  favourable  to  retentiveness  than  is  the  simple 
structure  we  have  been  discussing  here. 

§180.  Hysteresis  and  the  Dissipation  of  Energy. — The 
molecular  theory  shows  that  hysteresis  is  to  be  expected  when- 
ever the  magnetism  of  iron  is  caused  to  alter  through  anything 
more  than  a  very  narrow  range.  It  occurs  when  the  molecular 
movements  are  sufficiently  great  to  involve  the  breaking  up  of 
old  ties,  and  the  formation  of  new  ones,  on  the  part  of  some,  at 
least,  of  the  molecules.  In  other  words,  the  necessary  and 
sufficient  condition  for  hysteresis  is  that  there  must  be  an  un- 
stable phase  in  the  movement  of  some  of  the  molecules.  The 
change  of  magnetism  will  then  lag  behind  the  exciting  cause 
of  the  change,  whatever  that  may  be. 

When  the  change  is  restricted  within  very  narrow  limits 
there  is  no  hysteresis,  for  the  molecular  movements  are  then  of 
the  quasi-elastic  type,  occurring  without  rupture  of  the  mole- 
cular ties.  A  very  weak  magnetic  force,  applied  and  removed 
(whether  acting  alone  or  superposed  on  a  steady  force),  or  a  very 
small  change  of  mechanical  strain,  will,  if  it  be  many  times 
repeated,  cause  small  changes  of  magnetism  which  do  not  involve 
hysteresis,  because  the  molecular  magnets  are  then  suffering 
deflections  with  respect  to  which  they  are  stable.  But  when 
the  action  is  extended  by  using  larger  magnetic  forces  or  larger 
variations  of  mechanical  strain,  so  that  the  molecules  are  deflected 
far  enough  to  become  unstable,  hysteresis  comes  into  play.  We 
find  hysteresis,  in  fact,  manifesting  itself  in  all  save  the 
narrowest  cycles  of  magnetising  force,  of  longitudinal  pull,  of 
torsional  strain,  and  so  on. 

§181.  Rotation  in  a  Magnetic  Field.  Disappearance  of 
Hysteresis  when  the  Field  is  Strong. — The  molecular  theory 
outlined  in  §171  receives  striking  confirmation  from  experiments 


ROTATION    IN    A    MAGNETIC    FIELD.  327 

on  the  hysteresis  due  to  rotation  in  a  magnetic  field.  In. 
ordinary  processes  of  magnetic  reversal  the  field  is  reduced  to 
zero  and  is  then  re-applied  in  the  opposite  sense.  But  reversal 
may  also  take  place  through  a  rotation  of  the  field  relatively 
to  the  iron,  or  of  the  iron  relatively  to  the  field,  while  the  field 
preserves  a  constant  intensity.  In  fields  whose  force  is 
moderate,  such  rotation  involves  the  breaking  up  of  molecular 
groups  in  much  the  same  way  as  that  which  occurs  during  a 
reversal  of  the  field .  The  magnetic  molecules,  constrained  by  the 
force  which  they  exert  on  one  another,  pass  through  conditions 
of  instability  and  their  movements  involve  dissipation  of 
energy.  Measurements  of  the  work  expended  in  causing  a 
laminated  cylinder  of  iron  or  steel  to  revolve  between  the  pole 
of  a  magnet  show  that,  for  moderate  magnetic  forces,  more 
energy  is  dissipated  in  this  mode  of  reversal  than  in  the  other.* 
According  to  Prof.  Baily's  experiments  it  may  be  as  much  as 
fifty  per  cent,  greater,  when  the  force  is  such  as  to  produce  an 
induction  not  exceeding  10,000  C.-G.-S.  units.  But  when  the 
induction  rises  to  about  15,000,  the  hysteresis  in  the  rotating 
iron  passes  a  maximum;  after  which  it  diminishes  rapidly,  with 
the  result  that,  with  an  induction  of  20,000  or  so,  it  practically 
disappears  and  there  is  almost  no  work  spent  in  rotating 
the  iron. 

This  very  remarkable  result  was  predicted  by  Mr.  James 
Swinburne  as  a  consequence  of  the  author's  molecular  theory. 
Imagine  a  model  consisting  of  a  group  of  pivoted  magnets 
placed  near  enough  to  one  another  to  allow  their  mutual  forces 
to  take  effect,  and  suppose  a  strong  directing  field  to  be  applied 
to  it  with  the  result  that  the  magnets  are  brought  into  sensibly 
perfect  alignment,  corresponding  in  iron  to  the  condition  of 
saturation.  Then  suppose  the  model  to  be  slowly  turned 
round  while  the  strong  field  is  maintained  in  action.  Each 
little  magnet  will  simply  turn  with  the  field,  preserving  its 
direction  along  a  line  of  force,  forming  no  ties  with  its 
neighbours,  and  showing  no  tendency  to  be  set  into  oscillation. 
There  is  no  breaking  up  of  stable  groups  and  no  passage 
through  unstable  phases  in  the  motion.  In  other  words  the 
group  as  a  whole  exhibits  no  hysteresis.  But  when  the  field 

*  Baily,  "  On  the  Hysteresis  of  Iron  and  Steel  in  a  Rotating  Magnetic 
Field,"  Phil.  Trans.,  1896,  Vol.  187,  p.  715. 


328 


MAGNETISM  IN  IRON. 


is  sufficiently  reduced  the  inter-molecular  forces  resume  their 
ascendancy,  stable  combinations  are  formed  and  broken  as  the 
rotation  of  the  group  proceeds,  and  work  has  consequently  to 
be  spent  in  keeping  up  the  rotation. 

The  conclusion  that  hysteresis  should  vanish  when  iron  is 
rotated  in  a  very  strong  field  seemed  at  first  so  improbable 
that  it  was  advanced  by  way  of  criticism  of  the  author's 

30,000 


FIG.  151A. 

molecular  theory.  Mr.  Baily's  demonstration  that  hysteresis 
does,  in  fact,  nearly  vanish  may  be  claimed  as  going  far  to 
prove  its  fundamental  soundness.* 

Fig.  151  A  shows  Mr.  Baily's  results  for  soft  iron.  The 
Curve  I.  gives  the  relation  of  the  hysteresis  loss  to  B  when  the 
magnetic  force  was  reversed  in  the  usual  fashion,  and  Curve  II. 
gives  this  relation  when  the  reversals  occurred  through  rotation 

*  Mr.  Baily's  results  are  supported  by  the  experiments  of  Messrs. 
Beattie  and  Cliiiker,  The  Electrician,  Oct.  2,  1896. 


INFLUENCE   OF    MOLECULAR   AGITATION.  329 

of  the  iron  in  the  field.  It  will  be  noticed  incidentally  that 
in  Curve  I.  the  rate  of  increase  of  hysteresis  with  respect  to 
B  becomes  much  reduced  when  the  iron  is  highly  saturated — 
a  result  which  illustrates  the  fact  that  the  Steinmetz  formula 
(§  83a)  has  no  application  to  such  conditions. 

§  182.  Reduction  of  Hysteresis  by  Vibration,  &c.,  and 
other  Disturbances.— We  heave  seen  (§§  84,  85,  129)  that 
mechanical  vibration  lessens  the  differences  of  magnetic  condi- 
tions that  are  brought  about  by  hysteresis.  It  makes  the 
metal  readier  to  respond  to  any  influence  which  tends  to  alter 
the  magnetism.  In  a  soft  iron  wire,  where  its  effects  are  most 
conspicuous,  it  practically  abolishes  the  distinction  between 
what  we  have  called  the  first  and  second  stages  of  the  magne- 
tising process,  it  destroys  the  retentiveness  almost  entirely, 
and  it  makes  the  magnetic  effects  of  strain  nearly  reversible,  so 
that  the  u on"  and  "off"  curves  for  a  cycle  of  loading  come  to 
be  not  far  from  coincident. 

The  molecular  theory  makes  all  this  intelligible.  Vibration, 
producing  small  periodical  displacements  of  the  molecular 
centres,  sets  the  molecular  magnets  oscillating.  The  displace- 
ment of  the  centres,  and  still  more,  perhaps,  the  oscillation  to 
which  that  gives  rise,  allows  the  molecules  intervals  of  com- 
parative freedom,  and  probably  even  goes  so  far  as  to  vary  the 
combinations  in  which  they  are  grouped.  Then  if  there  is  an 
external  field  the  molecules  yield  readily  to  it  in  their  freer 
intervals,  and  even  when  there  is  no  external  field  a  kind  of 
shuffling  goes  on,  one  effect  of  which  is  to  reduce  residual 
magnetism.  It  may  be,  that  in  the  removal  of  residual  mag- 
netism vibration  acts  in  the  first  place  locally ;  a  cluster  of 
molecules  shaken  up  so  that  the  residual  magnetism  of  the 
cluster  is  less  than  that  of  surrounding  portions  will  act  to 
some  extent  like  a  cavity  in  the  metal,  producing  a  demag- 
netising field  round  about  it.  In  the  same  way  the  demagneti- 
sation of  a  long  iron  rod  under  vibration  no  doubt  begins  at 
and  about  the  ends,  where  there  is  a  self-demagnetising  field, 
and  then  extends  itself  towards  the  central  portion. 

Any  kind  of  disturbance  that  will  give  the  molecular  mag- 
nets intervals  of  freedom,  or  of  diminished  constraint,  will  tend 
to  do  away  with  hysteresis.  Interesting  examples  of  this  will 


380  MAGNETISM    IN    IRON. 

be  found  in  a  Paper  by  G.  G.  Gerosa  and  G.  Finzi*  in  which 
experiments  are  described  showing  how  cycles  of  reversal  of 
magnetism  become  modified  when  a  continuous,  or  periodically 
interrupted,  or  alternating  current  is  made  to  traverse  the 
piece  under  test,  while  slow  reversal  of  the  field  goes  on.  The 
experiments  dealt  with  iron,  steel,  and  nickel  wire  in  their  an- 
nealed and  hard  state.  A  continuous  current,  traversing  the 
,vire  while  its  longitudinal  magnetism  was  being  changed  by 
applying  and  varying  a  longitudinal  magnetic  force  by  means 
of  a  surrounding  solenoid,  was  found,  as  might  be  expected,  to 
reduce  the  susceptibility  of  iron  :  the  circular  magnetisation 
maintained  by  the  current  in  the  wire  left  the  molecules 
less  than  their  usual  freedom  to  obey  the  longitudinal  force. 
When  the  longitudinal  current,  instead  of  being  continuous, 
was  rapidly  interrupted  without  changing  its  sign,  a  mole- 
cular oscillation  was  set  up  which  made  the  iron  more 
than  usually  susceptible  to  weak  longitudinal  forces  ;  but 
when  the  field  was  strengthened  the  iron  was  still  found 
to  be  less  susceptible  than  when  no  current  was  passing 
through  it.  The  mere  make  and  break  of  the  longitudinal 
current  would,  in  fact,  cause  no  more  than  a  smajl  variation 
of  circular  magnetisation,  and  would  consequently  do  little 
to  agitate  the  molecules.  But  when  a  rapidly  alternating 
current  of  moderate  strength  traversed  the  wire,  the  suscep- 
tibility to  longitudinal  magnetisation  was  notably  increased ; 
the  magnetisation  curve  was  found  in  that  case  to  lie  above 
the  normal  curve  everywhere  except  in  the  region  of  strongest 
magnetisation.  The  violent  agitation  which  was  brought 
about  by  rapid  reversals  of  circular  magnetism  destroyed 
nearly  all  trace  of  hysteresis,  and  obliterated  the  usual  dis- 
tinctions between  successive  stages  in  the  magnetising  process. 
An  illustration  is  given  in  Table  XXXII.  and  Fig.  152, 
which  relate  to  an  experiment  in  which  a  piece  of  soft  iron 
wire,  0'84mm.  in  diameter,  was  magnetised,  first  under  the 
usual  conditions  (without  any  longitudinal  current),  and  then 
when  traversed  by  a  rapidly  alternating  current  of  three 
amperes. 

*  Kendiconti  del  R.  Istituto  Lombardo.  Vol.  XXIV.,  fasc.  x.,  April, 
1891.  See  also  a  Paper  by  Dr.  Finzi  in  The  Electrician,  April  3,  1891, 
p.  672. 


SUPPRESSION    OS1   HYSTERESJS. 


331 


Table  XXXII. — Magnetisation  of  Iron   U'itli  and   without   an 
alternating  longitudinal  current. 


Without  current. 

With  current. 

H 

1 

H 

1 

1-43 

50 

0-17 

75 

2-24 

119 

0-82 

290 

3-62 

367 

4-33 

803 

576 

773 

12-3 

1,178 

12-5 

1,162 

42 

1,537 

42 

1,500 

0 

76 

0 

1,121 

2468        10       12        14        16  H 


In  Fig.  152  the  curve  a  is  the  normal  curve,  and  b  is  the 
curve  obtained  when  the  alternating  current  was  in  action. 
The  table  shows  how  little  residual  magnetism  is  left  in  the 
second  case. 

Fig.  153  exhibits  in  the  same  way  the  influence  of  the  alter 
nating  longitudinal  current  on  a  cycle  in  which  the  longitudinal 
magnetism  of  another  iron  wire  was  reversed.  The  normal 
figure  a  a  collapses,  as  an  effect  of  the  molecular  shaking,  into 
b  b,  which  is  very  nearly  a  single  curve. 

Effects  of  the  same  kind  were  observed  in  steel  and  in  hard 
iron,  but  the  suppression  of  hysteresis  was  less  complete. 


332 


MAGNETISM    IN    IRON. 


The  single  curve  by  which  the  relation  of  I  to  H  may  be 
represented  when  hysteresis  is  done  away  with  by  sufficiently 
violent  agitation  of  the  molecules,  may  be  expressed,  with  fair 
accuracy,  by  the  formula 


in  which  a  and  /3  are  constants  for  a  given  specimen,  and  - 
is  the  saturation  value  of  I.     This  formula,  which  was  pro- 


600 


1200 


10 


8        10  H 


posed  by  Lamont  and  Frbhlich  as  a  general  means  of  ex- 
pressing the  relation  of  magnetism  to  field,  is,  of  course,  of 
no  service  so  long  as  hysteresis  is  operative,  since  I  then  depends 
not  only  on  the  existing  value  of  H  but  on  previous  values  :  it 
will  not  even  serve  to  express  the  curve  of  initial  magnetisation 
in  a  virgin  piece.  But  when  hysteresis  is  eliminated,  as  in 
these  experiments,  it  may  be  made  to  fit  the  curve  reasonably 
well.  Values  of  the  constants  a  and  /?  will  be  found  in  the 
Paper  from  which  these  results  are  quoted. 


EFFECTS   OP   TEMPERATURE.  333 

§  183.  The  Molecular  Theory  and  the  Effects  of  Tempera- 
ture.— To  see  the  bearing  of  the  molecular  theory  on  experi- 
mental results  regarding  the  effects  of  temperature  on  mag- 
netic quality,  we  have  to  revert  to  Figs.  79,  80,  and  81,  §  111, 
which  show  Hopkinson's  determination  of  the  permeability  of 
iron  at  various  temperatures,  for  a  small,  a  moderate,  and  a  fairly 
strong  magnetic  force  respectively.  In  the  first  of  these  figures 
(Fig.  79)  the  magnetic  force  is  only  0'3,  and  consequently  the 
susceptibility  at  ordinary  temperatures  has  the  comparatively 
small  value  which  we  expect  to  find  in  the  first  stage  of  the  mag- 
netising process.  As  the  temperature  is  raised  the  susceptibility 
increases,  at  first  but  slightly,  until  a  temperature  of  about 
600°C.  is  passed.  Then  the  rise  in  susceptibility  becomes 
very  rapid.  It  quickly  increases  more  than  ten-fold,  show- 
ing that  the  effect  of  this  heating  is  to  bring  on  the  second 
stage  of  the  magnetising  process.  Finally,  at  a  temperature  of 
775°C.  or  so  there  is  an  extraordinarily  sudden  fall  of  suscepti- 
bility, so  sudden  and  complete  that  when  the  temperature 
reaches  785°C.  practically  all  magnetic  quality  is  lost. 

Under  a  moderate  force  (of  4  C.-G.-S.  units,  see  Fig.  80)  there 
is  none  of  the  sudden  rise  of  susceptiblity  during  heating  which 
occurred  when  the  force  was  weak.  This  is  because,  under  the 
stronger  magnetic  force,  the  second  stage  in  the  magnetising 
process  had  already  been  entered  before  the  piece  was  heated. 
Further,  the  loss  of  susceptibility  at  high  temperature  occurs 
much  more  gradually.  Still  more  is  this  the  case  when  the  field 
is  comparatively  intense  (Fig.  81). 

The  first  effect  of  heating  is  to  hasten  the  transition  from 
the  first  to  the  second  stage  of  the  magnetising  process,  that 
is  to  say,  to  make  this  transition  occur  at  lower  values  of  the 
magnetic  force.  This  is  probably  due  to  two  causes.  Heating 
expands  the  structure,  and  that  weakens  the  ties  between  the 
molecules  by  increasing  the  distances  between  their  centres. 
We  may  conjecture  that  it  also  sets  up  oscillations  which 
contribute  to  make  the  ties  be  more  easily  broken.  When  the 
field  is  weak,  so  that  the  second  stage  has  not  been  reached 
while  the  metal  is  cold,  heating  is  consequently  favourable  to 
magnetisation,  and  with  an  appropriate  relationship  of  tempera- 
ture to  field  the  metal  is  in  a  critical  state,  in  which  a  small 
rise  of  temperature  produces  an  immense  augmentation  of 


S34  MAGNETISM    IN    IRON. 

susceptibility  by  making  groups  of  molecules  which  were  stable 
at  the  lower  temperature  become  unstable  at  the  higher. 

This  effect  of  heating  cannot  occur  if  the  field  is  strong 
enough  to  have  upset  most  of  the  molecules  before  heat  is 
applied.  Hence  the  curve  of  Fig.  80  has  no  sharp  apex  like 
that  of  Fig.  79. 

The  case  of  a  fairly  strong  field  is  more  simple.  Heating  has 
two  antagonistic  influences.  On  one  hand,  the  alignment  of  the 
molecular  magnets  is  still  being  facilitated  by  the  weakening 
of  their  mutual  forces.  On  the  other  hand,  the  oscillations 
which  they  acquire  have  virtually  the  effect  of  reducing  the 
moment  of  each  molecule.  Throughout  a  wide  range  of  tem- 
perature the  two  influences  nearly  counterbalance  one  another ; 
the  curve  in  Fig.  80  or  Fig.  81  is  nearly  level  for  a  great 
part  of  its  course;  but  as  the  temperature  becomes  rather  high 
the  prejudicial  effect  becomes  stronger,  and  the  curve  bends 
down. 

At  this  stage  the  molecules  seem  to  acquire  oscillation  very 
rapidly,  and  a  plausible  conjecture  to  account  for  the  complete 
loss  of  magnetic  quality  which  ensues  when  the  temperature 
rises  a  little  higher,  whether  the  field  be  weak  or  strong,  is 
that  the  oscillation  then  becomes  so  violent  as  to  develop  into 
rotation. 

The  establishment  of  this  rotation  would  account  for  the 
energy  which  we  know  to  be  absorbed  during  heating,  while  the 
iron  passes  from  the  magnetic  to  the  non-magnetic  state ;  and 
the  rapid  subsidence  of  this  rotation  into  oscillations  of  com- 
paratively narrow  range,  during  cooling,  would  in  the  same 
way  account  for  the  energy  which  the  iron  then  gives  out  as 
it  recovers  its  power  of  being  magnetised  (§  109). 

§  184.  Time-Lag  in  Magnetisation. — The  phenomena  of 
magnetic  viscosity,  described  in  §§  88  and  89,  have  some  light 
thrown  on  them  by  the  molecular  theory.  We  saw  that  when 
a  weak  magnetic  force  is  applied  to  soft  iron,  or  is  raised  a 
step,  the  resulting  change  in  the  magnetism  is  not  completed 
instantly.  There  is  a  protracted  creeping  up  of  the  magnetism, 
which  goes  on  long  after  the  magnetic  force  has  become 
constant.  We  saw  that  the  softness  of  the  iron  and  the  thick- 
ness of  the  specimen  had  a  great  influence  on  the  extent  of  this 


EFFECTS   OF   PERMANENT   SET.  335 

time-lagging.  A  piece  of  hard  iron,  or  a  very  thin  piece  of 
soft  iron,  showed  little  or  no  lag ;  a  thick  piece  of  soft  iron 
showed  much,  especially  when  the  experiment  was  made  at  an 
early  part  of  the  second  stage  (stage  B,  Fig.  136)  of  the  mag- 
netising process. 

It  appears  probable  that  an  explanation  of  this  is  to  be 
found  by  referring  to  the  part  that  is  played  by  the  inertia 
of  the  molecules  during  the  development  of  instability  in 
molecular  groups.  The  process  of  breaking  up  the  primitive 
configuration  takes  time.  The  disturbance  begins  at  a  point 
where  the  primitive  constraint  is  comparatively  weak,  and 
then  slowly  spreads  itself  even  when  the  deflecting  force  is 
kept  constant.  An  outlying  molecule  is  first  upset ;  then 
its  neighbours,  weakened  by  the  loss  of  its  support,  follow 
suit,  and  the  action  propagates  itself  from  moleeule  to  molecule 
throughout  the  group.  The  surface  molecules  may  be  con- 
jectured to  be  the  least  securely  held,  and,  therefore,  to  be  the 
first  to  yield.  In  a  very  thin  piece  of  iron,  such  as  a  fine  wire, 
there  are  so  many  surface  molecules  in  proportion  to  the  whole 
number,  and  consequently  so  many  points  that  may  become 
origins  of  disturbance,  that  the  breaking-up  of  the  molecular 
communities  is  too  quickly  completed  to  allow  much  of  this 
lagging  to  be  noticed.  Again,  when  iron  is  hardened  by  me- 
chanical strain  the  structure  ceases  to  be  even  approximately 
homogeneous  ;  the  molecules  become  as  it  were  parcelled  out 
into  small  groups  with  too  few  members  to  require  much  time  for 
the  spreading  of  the  disturbance  through  a  group,  and  in  that 
case  also  the  lagging  is  scarcely  perceptible  (see  §  185,  belcw). 

§  185.  Effects  of  Permanent  Mechanical  Strain. — It  was 
shown  in  §  66  that  when  a  piece  of  iron  is  hardened  by  being 
strained  sufficiently  to  take  permanent  set,  the  curve  of  I  and 
H  assumes  a  rounded  form  which  allows  this  condition  of  the 
metal  to  be  readily  distinguished  from  that  of  an  annealed 
piece.  The  successive  stages  of  the  magnetising  process,  in 
the  hardened  metal,  become  much  blended.  No  part  of  the 
curve  has  nearly  so  steep  a  gradient  as  we  find  in  dealing  with 
annealed  iron.  The  susceptibility  is  less  throughout,  and  satu- 
ration is  approached  with  greater  difficulty.  There  is  much 
less  retentiveness  ;  on  the  other  band,  there  is  much  more 


836  MAGNETISM    IN    IRON. 

coercive  force.  We  may  refer  back,  in  illustration  of  these 
differences,  to  Fig.  34,  §  66,  where  the  curves  for  a  cyclic  pro- 
cess of  reversal  are  drawn  side  by  side  for  the  same  piece  of  iron 
in  the  annealed  and  hardened  states. 

These  differences,  regarded  in  connection  with  the  molecular 
theory,  seem  to  indicate  that  mechanical  set  resolves  a  struc- 
ture which  is  relatively  homogeneous  and  continuous  into  one 
which  may  be  described  as  a  patchwork  of  more  or  less  distinct 
molecular  groups.  Hardening  the  metal  by  set  makes  only  a 
slight  change  in  the  density,  and  it  appears  probable  that  it 
brings  some  of  the  molecules  closer  together,  while  the  intervals 
between  others  are  widened,  with  the  result  that  groups  aro 
formed  in  which  the  intermolecular  forces  between  members  of 
any  one  group  are  stronger  than  the  forces  which  are  exerted 
across  the  wider  gaps  between  members  of  different  neighbour- 
ing groups.  The  "gaps"  tend  to  shear  over  the  curve  of  I  and 
H,  to  round  the  outlines  of  the  curve,  and  to  reduce  the  residual 
magnetism.  The  closeness  of  the  members  within  each  group 
increases  the  coercive  force.  Thus,  without  any  necessary 
change  in  the  density  of  the  mi-tal,  this  modification  of  the 
structure  would  bring  about  the  alteration  in  magnetic  quality 
which  is  observed.  Another  consideration  lends  some  support  to 
this  view.  In  hard  metal  there  is  exceedingly  little,  if  any,  "time- 
lag  "in  magnetisation.  The  explanation  of  "time-lag"  suggested 
in  the  last  paragraph  seems  to  require  that  the  structure  of 
annealed  iron  be  continuous  throughout  platoons  of  many  mole- 
cules. As  soon  as  the  platoons  are  split  up  into  little  groups 
the  action  described  there  cannot  be  expected  to  take  place. 

In  connection  with  this  it  may  be  remarked  that  any  inter- 
ruption of  the  continuity  of  the  molecular  structure  tends  in 
some  measure  to  shear  over  the  diagram  of  I  and  H,  and,  in  par- 
ticular, to  reduce  residual  magnetism,  by  making  the  conditions 
of  constraint  of  molecules  at  and  near  the  boundary  differ  from 
those  of  molecules  far  from  the  boundary.  It  seems  probable 
that  this  consideration  gives  a  clue  to  the  "  magnetic  resist- 
ance" of  joints,  described  above  in  §§  162-165.  Let  the  separated 
parts  of  a  cut  bar  be  ever  so  well  fitted  together,  the  molecules 
at  the  boundary,  and  for  some  little  distance  from  it,  are  not 
subject  to  the  same  conditions  of  constraint  as  subsist  in  the 
uncut  bar, 


REPETITION   OP   MAGNETIC   PROCESSES.  337 

§  186.  Effects  of  Repetition  of  Magnetic  Processes. — Space 
may  be  found  here  to  refer  shortly  to  one  or  two  of  the  minor 
phenomena  of  magnetisation,  which  the  molecular  theory  goes 
far  to  make  intelligible. 

A  consequence  of  the  irreversible  displacements  which  the 
molecular  magnets  suffer,  together  with  the  fact  that  the 
stability  of  each  molecule  depends  on  the  configuration  as- 
sumed by  many  molecules  in  its  neighbourhood,  is  that  in 
general  a  magnetising  process  has  to  be  repeated  more  than 
once  before  its  effects  become  strictly  cyclic.  In  some  cases  a 
progressive  change  may  be  traced  even  during  many  repe- 
titions of  the  process. 

For  instance,  let  a  magnetising  force  be  applied  to  a  piece  of 
soft  iron,  the  strength  of  the  field  being  regulated  so  that  it 
brings  the  metal  into  what  we  have  called  the  second  stage  of 
the  magnetising  process,  when  many  of  those  molecules  which 
are  not  already  upset  are  on  the  verge  of  being  upset.  Let  the 
force  then  be  removed  and  reapplied.  The  configuration  of  the 
group  during  this  re-application  is  by  no  means  the  same  as  it 
was  during  the  first  application,  and  accordingly  we  may  expect 
that  some  of  the  molecules  which  were  just  able  to  stand  in  the 
first  instance  yield  in  the  second  owing  to  the  changes  which 
have  meanwhile  taken  place  in  the  grouping  of  their  neigh- 
bours. The  re-application  of  the  magnetising  force  may  there- 
fore be  expected  to  produce  a  somewhat  stronger  magnetisation 
than  was  produced  when  the  force  was  first  applied.  To  a  less 
degree,  a  third  application  of  the  force  should  make  the  mag- 
netisation rise  a  little  higher  still,  and  so  on. 

Similarly,  the  second  removal  of  the  force  should  leave  more 
residual  magnetism  than  is  left  after  the  first  removal.  But 
we  may  expect  that  the  limits  between  which  the  magnetism 
changes  when  the  magnetising  force  is  applied  and  removed 
will  come  to  be  closer  in  each  repetition  of  the  process ;  the 
molecular  "  accommodation  "  which  goes  on  as  one  after  another 
of  the  doubtful  molecules  is  upset  has  the  effect  of  narrowing 
the  range  through  which  the  magnetism  alters  in  succeeding 
cycles. 

That  these  anticipations  are  in  accord  with  the  results  of 
experiment  will  be  seen  from  the  following  paragraphs,  mainly 
extracted  from  a  Paper  which  was  written  without  reference 


338 


MAGNETISM  IN  IRON. 


to  the  light    which   the   molecular   theory   throws    upon   the 
matter.* 

When  a  magnetising  force  is  first  applied,  then  removed,  and 
then  re-applied,  whether  suddenly  or  gradually,  theresulting  value 
of  I  is  somewhat  higher  than  that  reached  by  the  first  application. 
A  third  application  gives  a  somewhat  higher  value,  and  so  on, 
the  effects  apparently  approaching  an  asympotic  limit.  This 
appears  to  have  been  first  shown  by  the  experiments  of  Fromme.f 
At  each  removal  of  the  magnetising  force  the  residual  mag- 
netism is  also  left  somewhat  greater  than  before.  And  this 
second  action  (the  increase  of  the  residual  magnetism)  exceeds 
the  increase  of  the  induced  magnetism,  with  the  result  that  the 
changes  of  magnetism  between  residual  and  induced  diminish 
in  range  with  successive  removals  and  re-applications  of  the 
magnetising  force. 

The  following  observations  (Table  XXXIII.)  were  made  by 
the  ballistic  method  on  a  long  piece  of  soft  annealed  iron  wire. 
The  readings  are  given  without  reduction  to  absolute  measure ; 
they  relate  to  a  point  which  falls  early  in  the  steep  part  of  the 
curve  of  magnetisation. 

Table    XXXIII. 


Magnetising  current. 

Throw  of 
ballistic 
galvano- 
meter. 

Magnetism. 

Induced. 

Kesidual. 

First  made           

203 
-53-6 
+  54-2 
-47-8 
+  487 
-457 
+  46-6 
-44-9 
+  46-1 
-44-0 
+  45-6 

-42-6 
+  43-1 

-39-5 
+  39-8 

203 
203-6 
204-5 
205-4 
206-6 
208-2 

149*-4 
155:8 
158:8 
160:5 
162:6 

broken     .    .  . 

made    

broken     ... 

made    

broken    

made    

broken    

made   . 

broken    

made   

After  many  makes  and  breaks  — 
broken     

made    

After  many  more  makes  and  breaks  — 

made    

*  Ewing,  Phil.  Trans.,  1885,  p.  570,  §§  54-58. 

t  Pogg.  Ann.,  Ergbd.,  vii.,  1875,  and  Wied.  Ann.,  iv.,  1878. 


REPEATED    MAGNETISATIONS. 


339 


Similar  results  were  repeatedly  obtained,  both  with  freshly 
annealed  wires  and  wires  from  which  a  previous  strong  mag- 
netism had  been  shaken  out  by  tapping.  In  curves  showing 
the  relation  of  B  or  I  to  H  the  same  thing  exhibits  itself  in 
what  may  be  called  the  over-closing  of  loops  formed  by  re- 
moving and  re-applying  a  given  value  of  H.  A  good  example 
of  this  is  furnished  by  Fig.  44,  §78,  which  shows  how  much 
more  considerable  the  action  now  spoken  of  is  at  early  than  at 
late  stages  of  the  magnetisation. 

The  following  experiment  (Table  XXXIV.)  dealing  also  with 
annealed  iron  shows  that  the  same  kind  of  action  occurred 
when  the  current  was  slowly  changed  by  the  liquid  rheostat 
of  Fig.  17,  §  41,  and  the  magnetism  was  determined  by  a 
magnetometer : — 

Table  XXXIV. 


Magnetising  current. 

H 

Magneto- 
meter 
deflec- 
tion. 

1 

In- 
duced. 

Resi- 
dual. 

Gradually  raised  to  

...  70 

2-46 
0 
2-46 
0 

2-46 
0 

93 
65 
97 
70 

103 

80 

298 

sib 

330 

208 
224 

256 

...    0 

,,         raised  to  

...  70 

,  ,        reduced  to   ... 

0 

Then  100  sudden  makes  and  breaks  — 

,,        reduced  to    

...    0 

Incidentally,  this  experiment  illustrates  another  point,  to  which 
attention  was  long  ago  directed  by  Von  Waltenhofen — that 
the  amount  of  magnetisation  gained  or  lost  by  applying  or 
removing  a  given  magnetising  force  is  greater  when  the  change 
of  force  is  sudden  than  when  it  is  gradual.  Other  instances 
of  the  same  thing  will  be  found  in  the  experiment  quoted 
below. 

When  a  magnetising  force  is  applied  and  then  repeatedly 
reversed,  the  changes  of  magnetism,  instead  of  being  strictly 
cyclic,  form  what  may  be  termed  unclosed  loops.  An  instance 
of  this  is  given  by  Fig.  52,  §  82,  which  shows  a  series  of  these 
unclosed  loops  in  the  magnetisation  of  steel  wire.  The  result 
is,  as  in  the  case  of  repeated  removals  and  reapplications  of 


340 


MAGNETISM    IN    IRON. 


magnetising  force,  that  successive  repetitions  of  the  process  give 
a  gradually  diminishing  range  of  magnetic  change.  This  action, 
like  the  one  just  described,  occurs  most  conspicuously  at  points 
in  the  early  part  of  the  curve  of  magnetisation.  The  observa- 
tions in  Table  XXXV.  were  made  specially  to  exhibit  it,  on  a 
piece  of  annealed  iron  wire,  400  diameters  long,  by  the  magneto- 
metric  method. 

Table  XXXV. 


Magnetising  current. 

Magneto  - 
meter 
deflection. 

Remarks. 

0 

0 

Gradually  raised  to 

+  190 
190 
+  190 
-190 

+  146 
-141 

+  127 
-133 

Here  there  is  gradual 
diminution  of  range. 
>  This  part  of  the  ope- 

reversed -^o 



+  190 
-190 

+  120 
-132 

ration   is   shown   in 
Fig.  154. 

Suddenly                        

+  190 
-190 
+  190 

+  124 
-136 
+  123 

fHere  there  is  an  in- 
1    crease  of  range  due 
I    to  the  suddenness  of 
|^  these  reversals. 

Fifty  double  reversals,  then  — 
Suddenly  reversed  to    +  190 
„       „      -190 

+  111 
-127 

(  But    after    repeating 
1    the  sudden  reversals 
•{    often     enough     the 
range     becomes 

(^  smaller  than  ever. 

f  And  a  gradual  repe- 

Then  gradually       ,,      

+  190 

+  108 

J    tition   of    the   cycle 

5  J                       >»              »            

-190 

-126 

I    causes  still  a  further 

L  reduction  of  range. 

In  the  first  part  of  the  above  operations,  during  the  five 
gradual  reversals  of  magnetising  force,  intermediate  readings 
were  taken,  which  enabled  the  curves  shown  in  Fig.  154  to  be 
drawn.  These  show  at  a  glance  the  manner  in  which  the 
range  of  magnetic  change  diminishes.  Sudden  reversals, 
following  on  these,  cause  at  first  an  increase  of  range,  thus 
illustrating  the  comparative  effects  of  gradual  and  sudden 
change  of  H,  but  on  being  repeated  many  times  they  reduce 
the  range  to  a  lower  value  than  before. 

The  same  piece  of  wire  was  next  subjected  to  a  magnetising 
force  about  five  times  greater  than  the  above,  and  was  then 
demagnetised  by  reversals.  Experiments  similar  to  the  above 


REDUCTION    OF    RANGE    IN    SUCCESSIVE    CYCLES. 


341 


were  then  made  on  it,  when  it  was  found  that  the  tendency  to  a 
diminution  of  range  with  repetition  of  a  cyclic  alteration  of  mag- 
netising force  had  disappeared.  The  diagram,  Fig.  155,  shows 
the  effect  of  applying,  reversing,  and  re  applying  the  same  mag- 
netising force  as  in  the  former  case,  after  the  wire  had  been 
demagnetised  by  reversals.  It  shows  that  the  changes  of  mag- 
netism are  now  cyclic.  The  same  result  was  given  by  other 
specimens,  which  when  freshly  annealed  gave  much  diminution 


FIG.  154. — Repetition  of  Magnetic  Cycles  in  Annealed  Iron  "Wire. 


of  range,  but  when  demagnetised  by  reversals  after  the  magne- 
tising force  had  been  raised  to  a  high  value,  were  found  to  have 
lost  this  property.  In  this  respect,  then,  a  wire  demagnetised 
by  reversals  differs  from  the  same  wire  in  its  primitive  annealed 
state.  It  will  be  seen,  too,  by  comparing  figures  154  and  155, 
that  the  unsymmetrical  susceptibility  with  respect  to  forces  of 
opposite  signs  which  exists  in  the  annealed  wire  has  given  place 
to  a  very  perfect  symmetry  after  demagnetisation  by  reversals. 


342 


MAGNETISM    IN    IRON. 


Re-annealing  the  wire  restored  all  the  characteristics  of  the  pri- 
mitive state. 

The  following  observations  (Table  XXXVI.),  made  with 
another  piece  of  annealed  iron  wire  at  a  part  of  the  curve  very 
sensitive  to  the  actions  now  spoken  of,  show  well  the  reduction  of 
range  by  reversals,  and  then  the  rise  of  magnetism,  induced  and 


-H 


-I 


H 


Fio.  155. — Cyclic  Process  in  Annealed  Iron  Wire  previously  demagnetised 
by  reversals. 

residual,  which  is  produced  by  successive  removals  and  re-applica- 
tions of  H.  This  last  occurs  in  a  very  marked  way  after  the 
range  of  magnetic  change  has  been  reduced  by  reversals  of  H. 
The  two  directions  of  the  current  will  for  brevity  be  distinguished 
as  A  and  B.  The  changes  were  sudden,  and  the  magnetism  was 
determined  by  the  direct  magnetometric  method.  A  want  of 
symmetry  is  very  noticeable  here  between  the  positive  mag- 
netisation due  to  the  current  A,  which  is  first  applied,  and  the 
subsequent  negative  magnetisation  due  to  the  equal  and  opposite 
current  B. 


MAGiNETlC   SET    IN    STEEL. 


343 


Table  XXXVI. 


Magnetising  Current. 

Magneto- 
meter 
deflection. 

Kemarks. 

MadeA                      

+  232 

B 

-110 

A  

+  180 

' 

B 

-101 

„     A  

+  172 

Diminution   of  range 

„     B  

-100 

by  reversals. 

Twenty  reversals,  then  — 
Made  B            

-   95 

„      A  

+  158 

Broke  A                                  

+  150 

Made  A                    

+  200 

Broke  A  

+  193 

Rise  of  magnetism  (in- 

IVIade A 

+  206 

duced  and  residual) 

BrokeA     

+  201 

}-  by     successive      re- 

Twenty  makes  and  breaks,  then-- 

+ 205 

movals  and  re-appli- 
tions  of  H. 

Made  A         

+  209 

1 

Then  reversals  again  — 
Made  B  

-105 

„     A  

+  178 

The     diminution     of 

Forty  reversals  then  — 
Made  A  

+  163 

>  range  by  reversals  is 
I    again  conspicuous. 

B... 

-105 

Broke  and  remade  B 

-136 

Ditto  twenty  times  

-175 

The  magnetisation  of  steel  exhibits,  even  more  than  that  of 
iron,  reduction  of  range  with  successive  reversals  of  H,  and 
want  of  symmetry  between  the  values  of  I  induced  by  suc- 
cessively applied  +  and  -  values  of  H.  Fig.  156  shows  the 
changes  of  magnetism  which  were  undergone  by  an  annealed 
steel  wire  wben  a  magnetising  force  of  15  C.-G.-S.  units  was 
applied,  removed,  re-applied,  reversed,  and  again  reversed  twice. 
The  want  of  symmetry  between  the  positive  and  negative 
values  of  tbe  magnetism  is  very  marked  in  this  example  :  the 
steel  acquires  a  strong  magnetic  set  towards  the  side  of  the 
first  magnetisation. 

§  187.  Effects  of  Elastic  Strain.— In  an  earlier  chapter 
(§§  120 — 142)  an  account  has  been  given  of  experiments  made 
to  investigate  the  effects  of  stress  on  the  magnetic  quality  of 


344 


MAGNETISM    IN    IKON. 


iron  and  the  other  magnetic  metals.  Without  attempting  any 
full  discussion  of  these  results  from  the  point  of  view  which 
the  molecular  theory  affords,  we  may  refer  to  one  or  two  general 
features  where  a  molecular  explanation  seems  comparatively 
easy. 

That  stress  should  produce  an  influence  on  magnetic  quality 
is  a  probable  result  of  the  strain  to  which  the  stress  gives  rise. 
The  effect  of  a  simple  longitudinal  stress  is,  as  we  have  seen, 
to  make  the  metal,  originally  isotropic  in  its  magnetic  quality, 


FIG.  156. — Repetition  of  Magnetic  Cycles  in  Annealed  Steel. 

become  scolotropic,  and  it  may  be  conjectured  that  this  happens 
through  differences  becoming  established  in  the  pitch  of  the 
molecular  magnets,  in  lines  respectively  along  and  across  the 
direction  of  the  stress,  whereby  old  lines  of  molecules  break 
up  and  new  lines  are  formed.  A  uniform  dilation  or  a  unifoi  m 
compression  (with  equal  intensities  of  stress  in  all  directions) 
might  be  expected  to  have  a  much  less  considerable  influence 
on  magnetic  quality  than  a  simple  stress  has.  Experiments 
on  the  effects  of  such  stresses  are  wanting ;  it  may  be  antici 


EFFECTS    OF    STRAIN.  345 

pated  that  effects  resembling  those  due  to  change  of  tem- 
perature would  be  observed.  Thus  we  might  expect  to  find 
a  uniform  pressure  in  all  directions  associated  with  a  general 
reduction  of  magnetic  susceptibility.  The  experiment  would  be 
an  interesting  one  to  carry  out,  especially  in  nickel,  where  (§  122) 
the  susceptibility  is  known  to  be  greatly  increased  by  a  single 
stress  of  compression  applied  in  the  direction  of  magnetisation. 

A  stress  of  simple  pull  will  lengthen  those  rows  of  molecules 
which  lie  more  or  less  along  the  axis  of  the  stress,  and  will 
shorten  those  rows  which  lie  more  or  less  across  the  axis. 
This  is  enough  of  itself  to  develop  differences  of  magnetic  sus- 
ceptibility in  the  longitudinal  and  transverse  directions ;  and 
the  difference  is  probably  much  intensified  by  a  re-arrange- 
ment of  the  molecular  rows,  the  longitudinal  rows  being  more 
or  less  broken  up  and  transverse  rows  formed.  The  length- 
ening of  the  longitudinal  rows  will  tend  to  increase  the  sus- 
ceptibility ;  the  shortening  of  the  transverse  rows,  and  still 
more  the  secondary  consequence  of  stress,  namely,  the  forma- 
tion of  new  transverse  rows,  will  tend  to  reduce  it.  It  seems 
that  in  nickel  the  reducing  effect  is  the  dominant  one  ;  in  iron, 
on  the  other  hand,  we  find  a  conflict  of  influences  which  makes 
pull  favourable  or  otherwise  according  as  the  magnetisation  is 
less  or  greater  than  a  critical  value. 

The  large  magnetic  changes  due  to  torsion  which  are  seen  in 
experiments  on  nickel,  such  as  the  reversal  of  magnetism  which 
Nagaoka  found  when  a  loaded  nickel  wire  was  twisted  to  and  fro 
to  alternate  sides  (§  142) — appear  to  be  secondary  effects,  due  to 
the  reconstruction  of  molecular  rows  which  become  unstable 
when  the  molecular  centres  are  displaced  by  the  strain.  It  is 
the  existing  magnetism  of  the  piece  that  is  being  affected, 
rather  than  its  susceptibility  to  induction  by  the  field. 

An  obvious  conclusion  from  the  molecular  theory  is  that  there 
should  be,  as  we  know  there  is,  hysteresis  in  the  changes  of 
magnetic  quality  that  are  associated  with  changes  of  stress,  and 
also  that  the  condition  arrived  at  by  first  applying  a  load  and 
then  magnetising  should  in  general  be  different  from  the  condi- 
tion arrived  at  by  first  magnetising  and  then  applying  a  load. 
(See  §§  120—131.) 

Another  fact  which  the  molecular  theory  serves  to  explain  is 
the  important  difference  which  experiments  reveal  between 


346 


MAGNETISM    IN    IRON. 


260 


.240 


230 


the  effect  that  is  produced  by  the  first  application  of  a  stress, 
and  the  effect  that  is  produced  when  the  same  stress  is 
applied  after  it  has  been  previously  applied  and  removed 
many  times.  After  what  has  been  said  above  in  §  1 27,  a  brief 
reference  to  this  matter  will  suffice. 
Provided  the  magnetising  force  is  not 
very  strong,  the  first  application  of 
load,  when  the  piece  hangs  in  a  steady 
magnetic  field,  upsets  molecules  which 
were  nearly  upset  before  the  load  was 
applied.  Removal  of  the  load  does 
not  make  these  molecules  recover  the 
position  from  which  the  application 
of  the  load  disturbed  them.  Thus 
successive  loadings  and  unloadings, 
especially  in  a  weak  field,  serve,  as  it 
were,  to  shake  in  the  magnetism;  and, 
if  residual  magnetism  is  dealt  with, 
the  field  having  been  removed,  suc- 

g  A    I  cessive  loadings  and  unloadings  serve 

to  shake  it  out.  Examples  of  this 
have  already  been  given  in  Figs.  108 
and  109,  where  the  effects  of  a  first 
loading  and  unloading  are  readily 
distinguishable  from  those  that  oc- 
cur after  a  cyclic  regime  has  be- 
come established  by  repetition  of  the 
cycle  of  loads.  Fig.  119,  exhibit- 
ing certain  effects  of  successively  ap- 
plied twists  to  alternate  sides,  is  also 
an  instance  in  point.  When  we  load 
a  wire  in  a  strong  field  we  find,  as  the 
theory  would  lead  us  to  expect,  that 
the  cyclic  regime  is  quickly  attained ; 
a  second  loading  is  enough  to  show 
that  the  initial  disturbing  influence 

of  the  stress  is  exhausted.  In  weak  fields,  the  loading  has  to 
be  repeated  many  times  before  that  is  the  case,  and  the  first 
disturbance  is  sometimes  immensely  greater  than  the  alter- 
ation of  magnetism  that  accompanies  each  application  and 


O  l  2 

Load  %n  kilos. 

FIQ.  157.— Effects  of 
Loading  a  Soft  Iron  Wire 
in  a  Weak  Magnetic  Field. 


HYSTERESIS   IN    MOLECULAR    GROUPING. 


347 


removal  of  the  load  after  a  cyclic  condition  has  been  reached. 
Fig.  157  gives  an  example.  The  specimen  dealt  with  there 
was  a  long  wire  of  soft  annealed  iron,  0'76mm.  in  diameter, 
which  hung  in  a  weak  field  (H=0'34).  A  load  of  1  kilo- 
gramme applied  for  the  first  time  raised  the  magnetism  from 
159  to  220  (in  arbitrary  units).  Removal  of  the  load  reduced 
it  only  to  218.  Re-application  brought  it  up  to  222  ;  a  second 
removal  reduced  it  to  220J.  A  third  application  made  it  224, 
a  third  removal  222,  and  a  fourth  application  225J.  Then 
the  load  was  increased  to  2  kilogrammes,  and  the  magnetism 
went  up  at  a  bound  to  247,  after  which  successive  removals 
and  re-applications  of  that  load  produced  but  slight  changes 
which  tended  gradually  to  assume  a  cyclic  character  when  the 
operation  was  repeated  many  times.* 

§  188.  Hysteresis  in  Changes  of  Molecular  Configuration, 
apart  from  the  Existence  of  Magnetisation. — In  §§  133-135 
experiments  have  been  referred  to  which  show  that  when  iron 
is  subjected  to  cyclic  variation  of  stress,  its  structure  undergoes 
changes  that  involve  hysteresis,  even  when  no  magnetic  force 
acts  upon  it,  and  when  there  is  no  magnetisation  of  the  piece  as 
a  whole.  The  molecular  theory  makes  the  reason  of  this  suffi- 
ciently apparent.  Elastic  strain  brings  about  a  rearrangement 
of  the  molecular  grouping;  old  combinations  break  up  and  novel 
combinations  are  formed,  although  no  magnetic  forces  are  con- 
cerned other  than  the  forces  which  the  molecular  magnets 
exert  on  one  another.  These  changes  of  configuration  involve 
unstable  movements  on  the  part  of  the  molecules,  and  hysteresis 
consequently  manifests  itself,  when  the  piece  is  carried  through 
a  cycle  of  strain.  We  find,  for  instance,  that  when  an  iron  wire 
under  tension  is  loaded  and  unloaded,  by  putting  on  and  taking 
off  weights,  there  is  a  distinct  difference  in  the  physical  state 
of  the  metal,  under  one  and  the  same  intermediate  amount  of 
weight,  during  loading  and  during  unloading.  The  difference 
shows  itself  in  magnetic  susceptibility,  in  thermo-electric 
quality,!  and  possibly  in  many  other  physical  qualities  of  the 
material.  It  continues  to  be  found  when  the  cycle  of  loading 

*  For  details  of  this  and  other  experiments  illustrating  the  point  now 
referred  to,  see  Phil.  Trans.,  1885,  p.  594,  et  seq. 
t  See  a  Paper  by  the  Author,  Phil.  Trans.,  1886,  p.  361. 


348  MAGNETISM   IN    IRON. 

is  repeated,  and  its  character  is  just  such  as  the  molecular 
theory  would  lead  us  to  expect. 

This  hysteresis  in  molecular  configuration,  apart  from  all 
actual  magnetisation,  which  exhibits  itself  when  the  piece  is 
carried  through  a  cycle  of  elastic  strain,  has  one  important 
consequence.  It  implies  that  the  elasticity  of  the  substance  is 
not  perfect.  The  unstable  movements  of  the  molecules,  to 
which  it  is  to  be  ascribed,  result  in  a  dissipation  of  energy. 
More  work  has,  therefore,  to  be  spent  in  stretching  the  piece, 
while  loads  are  being  put  on,  than  is  recovered  when  the  loads 
are  taken  off — in  other  words,  the  stress  that  corresponds  to  any 
given  intermediate  value  of  the  strain  must  be  greater  during 
the  application  of  the  load  than  during  its  removal.  There 


FIG.  158. 

must  be  hysteresis  in  the  relation  of  strain  to  stress ;  and,  as 
we  have  seen  already  (§  135),  this  conclusion  is  borne  out  by 
experiment. 

§  189.  Experimental  Study  of  Molecular  Groups  by  means 
of  Models. — It  is  extremely  helpful,  in  considering  the  con- 
straint which  the  molecular  magnets  suffer  in  consequence  of 
their  polar  forces,  to  experiment  with  a  model  consisting  of  a 
number  of  short  steel  magnets,  pivoted  like  compass  needles  on 
fixed  centres,  and  placed  near  enough  to  one  another  to  allow 
their  mutual  control  to  be  felt.*  Such  a  model  is  readily  made 
out  of  pieces  of  stout  magnetised  steel  wire,  bent,  as  in  Fig.  158, 
to  bring  the  centre  of  gravity  below  the  pivot  point.  A  recess 
for  the  pivot  is  stamped  by  a  centre  punch  in  the  hollow  of  the 

*Proc.  Roy.  Soc.,  1890,  Vol.  XL VIII.,  p.  342  j  PhiL  Slag  ,  September,  1890. 


MODEL    ILLUSTRATING    MOLECULAR   THEORY.  349 

bend,  and  the  pivot  itself  is  a  needle  stuck,  with  the  point 
upwards,  in  a  small  block  of  lead  or  of  wood.  Instead  of  a 
wire,  a  piece  of  steel  plate  may  be  used  for  the  magnet,  and 
this  may  have  any  form  given  to  its  polar  extremities,  from 
sharp  points  to  semicircles.  The  magnets  being  of  hard  stee\ 
strongly  magnetised,  are  practically  unaffected  (as  to  the  intensity 
of  their  magnetism)  by  the  comparatively  weak  external  mag- 
netic  forces  which  are  applied  for  the  purpose  of  turning  them 
into  line.  The  external  force  may  be  applied  by  a  coil  wound  in 
an  open  manner  over  a  light  framework,  within  which  the  group 
of  magnets  is  placed,  the  open  winding  allowing  the  behaviour 
of  the  magnets  within  to  be  observed.  Or  a  larger  coil  placed 
entirely  underneath  the  group  may  be  used ;  or,  better  still,  a 
pair  of  closely-wound  short  coils  placed  one  on  either  side  of 
the  group.  This  last  form  is  especially  convenient  when  the 
behaviour  of  the  group  is  to  be  exhibited  by  projecting  them  on 
a  lantern  screen.  For  that  purpose  short  magnets  are  neces- 
sary, and  the  magnets  used  for  small  pocket  compasses  will  be 
found  very  suitable  ;  the  pivots  themselves  may  also  be  cut  out 
of  such  compasses  and  cemented,  at  proper  distances,  on  a  glass 
plate.  To  exhibit  the  effects  of  strain,  the  pivots  may  be 
arranged  on  a  framework  of  jointed  wooden  rods,  forming  two 
crossed  sets  of  parallel  lines;  by  placing  the  pivots  at  the 
joints,  or  midway  between  the  joints,  some  of  the  effects  of 
simple  shear  or  simple  pull  and  push  may  be  studied. 

Fig.  158A  shows  such  a  model,  in  which  the  field  is  produced 
by  two  coils  at  the  ends,  and  the  magnets  are  supported  on 
centres  cemented  to  a  sheet  of  glass,  which  may  bs  turned 
round  to  exhibit  effects  of  rotation. 

A  model  of  this  kind  allows  the  three  stages  of  the  mag- 
netising process  to  be  readily  distinguished.  The  phenomena 
attending  reversal  of  magnetism,  the  dissipation  of  energy  in 
hysteresis,  the  conditions  that  promote  residual  magnetism,  the 
comparative  effects  of  slow  and  sudden  changes  in  magnetic 
force,  the  primitive  and  final  effects  of  strain,  the  influence  of 
vibration,  the  existence  of  time-lag,  are  all  matters  of  which 
the  model  gives  effective  illustration. 

The  manner  in  which  the  resultant  polarity  of  the  group  of 
pivoted  magnets  changes  when  the  field  is  applied,  reversed,  or 
varied  in  any  way,  is  sufficiently  evident  on  mere  inspection  of 


350 


MAGNETISM    IN    IRON. 


the  group.  It  may,  however,  be  determined  quantitatively  by 
using  a  magnetometer  in  the  ordinary  way,  taking  care  to  com- 
pensate for  the  action  of  the  coil  which  supplies  the  magnetic 
field  by  placing  in  series  with  it  a  second  coil,  the  position  of 
which  is  adjusted  so  that  it  may  annul  the  deflection  which 
the  first  coil  by  itself  would  produce.  A  group  of  magnets 
examined  in  this  way,  when  carried  through  a  cycle  of  con- 
figuration by  applying  and  reversing  the  directive  force  of  the 
coil,  gives  what  we  may  call  curves  of  magnetisation,  in  which 
all  the  main  characteristics  of  the  ordinary  curves  for  iron 


FIG.  158A. 

appear,  though,  of  course,  the  limited  number  of  magnets 
which  it  is  practicable  to  use  in  such  an  experiment  makes  the 
steps  of  the  process  more  jerky  than  they  are  when  we  have  to 
deal  with  the  multitudes  of  molecules  in  a  piece  of  solid  metal. 
Curves  obtained  by  this  means,  showing  the  reversal  of  a  group 
of  twenty -four  little  magnets  (like  the  one  shown  in  Fig.  158) 
under  reversal  of  the  magnetising  field,  are  given  in  Fig.  159.* 

*  Fig.  159,  for  which  the  author  is  indebted  to  Mr.  Glazebrook,  repre- 
sents the  results  of  an  experiment  by  Mr.  J.  W.  Capstick,  made  in  answer 
to  a  question  set  in  the  practical  examination  of  the  Cambridge  Natural 
Science  Tripos.  1891.  Curves  of  this  kind  were  first  published  by  Mr.  Arthur 
Hoopes  in  the  Electrical  World  (New  York),  May,  1891.  See  The  Elec- 
tricifw,  May  29,  1891. 


EXPERIMENTS   WITH   GROUPS   OF    MAGNETS. 


351 


The  correspondence  between  the  curves  of  magnetisation  and 
those  got  from  a  group  of  little  magnets  becomes  even  closer 
when  the  number  of  magnets  in  the  group  is  largely  increased. 
In  experiments  by  Miss  Klaassen  and  the  author*  as  many  as 
130  magnets  were  used  to  form  the  group,  and  it  was  found 
that  not  only  the  main  features  of  the  magnetising  process, 
but  also  some  of  the  less  obvious  features  referred  to  in  §  186, 


FIG,  159. — Cyclic  Process  applied  to  a  Group  of  Twenty-four  Pivoted 

Magnets. 

were  reproduced  with  surprising  fidelity.  Thus,  for  instance, 
differences  resembling  those  illustrated  in  Fig.  154  are  found 
when  successive  cyclic  variations  are  made  to  take  place  in  the 
directing  field  to  which  the  group  is  exposed,  provided  the 
group  of  magnets  has  simply  been  left  to  settle  after  a 
casual  "shuffling."  But  if  the  group  has  previously  been 


Phil.  Trans.,  1894,  p.  1,036. 


352  MAGNETISM    IN    IRON. 

exposed  to  reversals  of  a  gradually  diminishing  directive 
orce,  the  subsequent  behaviour  resembles  that  of  the  iron  in 
Fig.  155. 

The  study  of  what  happens  in  a  group  of  small  magnets 
goes  to  confirm  the  theory  that  the  molecules  of  a  magnetic 
metal  are  controlled,  as  to  direction,  simply  by  the  forces 
which  they  exert  on  one  another  as  magnets,  and,  as  has 
been  pointed  out,  the  theory  receives  its  most  complete 
confirmation  when  the  group  is  made  to  revolve  in  a  strong 
directing  field, 

§  190.  Ampere's  Hypothesis  as  to  the  Nature  of  the  Mag- 
netic Molecules. — Granting,  as  we  very  well  may  (in  view  of 
the  considerations  summarised  in  this  chapter),  that  the  process 
of  magnetising  consists  in  turning  round  molecules  that  are 
already  magnetic,  so  that  their  axes  tend,  under  the  directing 
force  of  the  applied  field,  to  approach  a  particular  direction,  the 
question  still  remains,  to  what  is  the  primitive  magnetism  of 
the  molecules  due  ?  Weber's  theory  does  not  help  us  to  an  ex- 
planation of  the  fact,  which  it  postulates,  that  each  molecule  is 
a  permanent  magnet. 

According  to  the  hypothesis  of  Ampere  the  magnetism  of  the 
molecule  is  due  to  an  electric  current  continually  circulating 
within  it — in  other  words,  the  molecule  is  a  conducting  circuit 
in  which  a  current  flows,  and  when  a  directing  field  acts,  the 
channel  in  which  this  current  flows  tends  to  set  itself  at  right 
angles  to  the  direction  of  the  field,  just  as  does  the  coil  of  an 
electro-dynamometer.  Ampere's  theory,  therefore,  explains  all 
the  phenomena  of  magnetisation  as  consequences  of  the  mutual 
action  of  electric  currents.  According  to  it,  in  magnetising 
a  piece  of  iron  we  are  dealing  with  the  forces  which  exist 
between  the  current  in  an  external  conductor  and  the  currents 
in  molecular  circuits  within  the  metal,  which  are  prevented 
from  immediately  putting  themselves  into  perfect  parallelism 
with  the  external  circuit  only  because  of  the  forces  which  the 
currents  in  the  molecules  exert  on  one  another.  In  this  view 
the  model  of  a  magnetic  metal  should  be  constructed  by  using 
not  pieces  of  permanently  magnetised  steel  to  represent  the 
molecules,  but  little  coils,  free  to  turn,  in  each  of  which  an 
electric  current  flows  continually. 


HYPOTHESES    OP    AMPERE    AND    WEBER.  353 

The  molecular  channels  must  be  supposed  to  offer  no  resist 
ance  as  conductors,  otherwise  the  primitive  currents  would 
require  energy  to  be  expended  in  maintaining  them. 

When  a  field  is  applied  it  tends  to  turn  the  molecular  cir- 
cuits, and  it  also  induces  supplementary  currents  in  them. 
These  induced  currents  are  superposed  on  the  primitive  cur- 
rents ;  their  strength  depends  on  the  inclination  of  the  circuit 
to  the  field ;  and  their  general  effect  is  to  reduce  the  primitive 
currents.  Whether  they  will  do  so  to  any  considerable  extent 
depends  on  the  area  and  the  self-induction  of  the  molecular 
circuits,  and  on  the  primitive  strength  of  the  currents  in 
them.*  Thus  if  the  primitive  currents  are  strong  and  the 
other  conditions  favourable,  very  little  reduction  of  the 
primitive  strength  takes  place  through  this  induction  of 
current  by  the  applied  field.  In  that  case  the  molecular 
circuits  are  nearly  equivalent  to  strictly  permanent  magnets, 
and  merely  turn  in  response  to  the  field,  without  suffering 
any  material  loss  of  intensity.  Probably  this  represents 
what  occurs  when  iron  or  any  of  the  other  strongly  magnetic 
metals  is  magnetised. 

When  the  primitive  molecular  currents  are  weak  the  induction 
of  opposing  currents  by  the  application  of  a  magnetic  field  may 
modify  the  resultant  strength  very  greatly ;  and  in  particular, 
when  there  are  no  primitive  currents  at  all,  but  only  conduct- 
ing molecules  ready  to  have  currents  induced  in  them,  the 
application  of  the  field  will  induce  currents  which  give  to  tho 
piece  a  polarity  of  the  kind  opposite  to  that  which  it  acquires  in 
ordinary  magnetisation.  By  recognising  the  existence  of  these 
induced  currents  Weber  thus  extended  Ampere's  theory  of 
molecular  conducting  circuits  to  account  for  diamagnetism. 

But  even  when  there  are  strong  primitive  currents,  as  we 
must  suppose  there  are  in  the  molecules  of  iron,  the  induction 
of  opposing  currents,  in  consequence  of  applying  a  magnetic 
field,  will  go  on  to  some  extent,  and  there  is  a  stage  at  which 
its  influence  may  be  appreciable.  This  is  when  the  piece  is 
saturated — when  all  the  molecular  circuits  are  turned  into 
planes  perpendicular  to  the  direction  of  the  field.  In  that 
position  they  are  as  favourably  placed  as  possible  for  the 

*  See  Maxwell's  "  Electricity  and  Magnetism,"  Vol.  II.,  chap.  xxn. 

A  A 


354  MAGNETISM   IN   IRON. 

induction  in  them  of  currents  opposed  to  the  primitive  cur- 
rents. When  the  field  is  further  strengthened,  the  resultant 
current  in  each  molecular  channel  is  reduced,  and  as  the 
channels  are  already  all  perpendicular  to  the  field,  the  only  effect 
of  increasing  the  field  is  to  reduce  the  magnetisation  of  the  piece 
by  reducing  the  strength  of  each  molecule.  The  Ampere -Weber 
theory,  therefore,  leads  us  to  conceive  of  the  magnetism  of 
iron  as  tending  to  pass  a  limiting  value  when  saturation  is 
reached,  after  which  a  stronger  magnetising  force  should 
actually  weaken  the  magnetism.  The  results  of  experiments 
with  very  strong  fields  neither  confirm  this  nor  contradict  it. 
They  show  that  when  the  condition  of  saturation  has  been 
approached  the  field  may  be  strengthened  ten-fold  or  more 
without  any  material  change  in  the  magnetisation,  either  in 
the  way  of  addition  or  loss.  But  the  conditions  under  which 
such  experiments  are  carried  out  make  very  accurate  measure- 
ment impracticable,  and  a  small  reduction  of  the  magnetism 
might  pass  undetected.  It  is  probable  enough  that  stronger 
fields  still  must  be  used  to  discover  it,  for  the  reduction  which 
is  to  be  expected  as  a  consequence  of  induced  currents  in  the 
molecular  channels  is  slight  at  the  most,  and  in  the  approach 
to  saturation,  which  is  long  drawn  out,  the  continued  deflection 
of  the  molecules  tends  to  counterbalance  any  effect  that  may 
be  produced  by  a  small  loss  of  moment  on  the  part  of  each. 


CHAPTER    XII. 


PRACTICAL    MAGNETIC    TESTING. 

§  191.  Practical  Magnetic  Tests. — Of  the  various  methods 
of  magnetic  measurement  described  in  earlier  chapters,  a 
considerable  number  are  suited  only  for  use  in  laboratory 
research.  In  this  chapter  an  account  will  be  given  of  some 
methods  which  recent  experience  has  shown  to  be  useful 
where  the  problem  is  to  make  such  tests  of  iron  and  steel  as 
will  serve  the  purposes  of  the  electrical  engineer. 

The  ballistic  method,  in  one  form  or  another,  is  largely 
used  in  such  tests,  both  directly  and  for  the  purpose  of 
testing  standard  pieces  which  may  afterwards  be  used  in 
methods  of  testing  where  the  process  consists  in  simply 
comparing  the  specimen  under  examination  with  a  standard 
piece  whose  magnetic  quality  is  known  beforehand.  It  is 
scarcely  too  much  to  say  that  the  ballistic  method,  whether 
as  a  direct  means  of  testing  specimens  or  as  a  means  of 
testing  standards  to  be  used  in  comparison  with  specimens, 
is  the  basis  of  practically  all  workshop  tests  of  magnetic 
quality. 

The  materials  to  be  tested  are  chiefly  wrought  iron  and 
mild  steel  forgings  and  steel  castings,  for  permeability,  these 
metals  being  used  for  dynamo  field-magnets,  and  also  rolled 
sheets  of  iron  or  steel,  for  hysteresis  and  occasionally  for 
permeability,  these  forming  the  cores  of  transformers  and 
armatures.  The  "  steel"  castings,  which  are  now  very 
extensively  used  for  field-magnets,  consist  of  very  nearly  pure 
iron,  and  are  called  steel  only  because  they  are  made  not  by 
puddling,  but  by  a  modified  Bessemer  or  other  "  steel " 
process.  Much  of  the  sheet  metal  is  rolled  from  Swedish 
charcoal  iron,  but  sheet  metal  produced  by  steel  processes  is  also 

AA  2 


•356  MAGNETISM    IN    IRON. 

used  for  magnetic  purposes,  and  some  of  it  appears  to  have  more 
immunity  than  Swedish  iron  from  "  ageing  "  under  exposure 
So  prolonged  warmth.  The  sheet  metal  is  supplied  in  the 
form  of  annealed  stampings,  and  any  tests  should  be  made  on 
specimens  which  have  been  treated  in  the  same  way  as  the 
rest ;  that  is  to  say  the  test  pieces,  after  being  stamped  in  a 
form  appropriate  for  testing,  should  be  annealed  under  the 
same  conditions  as  other  stampings. 

In  permeability  tests  of  forgings  and  castings  for  dynamo 
magnets  it  is  generally  useful  to  obtain  data  for  a  curve 
giving  the  relation  of  B  to  H  from,  say,  B  =  10,000  to 
B  =  18,000.  The  lower  part  of  the  curve  is  not,  as  a  rule, 
wanted,  and  it  is  very  rarely  that  inductions  above  18,000  are 
in  question. 

In  hysteresis  tests  of  iron  or  steel  stampings  for  transformers 
a  knowledge  of  the  hysteresis  loss  in  a  cycle  where  the  limits 
of  B  are  about  4,000  will  generally  suffice,  the  formula  of 
Steinnietz  serving  sufficiently  well  to  calculate  from  that  the 
hysteresis  at  higher  or  lower  inductions  within  a  moderate 
range.  If,  however,  the  hysteresis  of  armature  stampings 
working  at  much  higher  induction  is  in  question,  it  is  more 
satisfactory  to  make  a  direct  determination  of  the  loss  in  a 
correspondingly  high  cycle  than  to  infer  the  loss  from  a  low 
cycle  measurement. 

Permeability  tests  are  not,  as  a  rule,  required  in  dealing 
with  transformer  iron.  There  the  question  of  hysteresis  is 
all-important,  and  a  material  which  is  good  in  respect  of 
hysteresis  may  safely  have  its  permeability  taken  for  granted. 
With  dynamo  stampings  the  question  of  permeability  under 
strong  or  moderately  strong  forces  comes  in,  just  as  it  does 
in  dynamo  forgings  or  castings,  and  similar  tests  are 
appropriate. 

§  192.  The  Ballistic  Method.— Fig.  160  shows  an  arrange- 
ment for  ballistic  tests  which  the  author  has  found  convenient. 
It  is  equally  applicable  to  tests  of  permeability  only  and  to 
tests  in  which  B-H  cycles  are  to  be  determined  in  order  to 
evaluate  the  hysteresis.  The  specimen  A  is  wound  with 
primary  and  secondary  coils,  which  are  shown  diagram- 
matically  on  separate  parts  of  the  ring  in  the  figure,  but  are 


BALLISTIC    TESTS    OP   RINGS. 


357 


actually  wound  in  a  uniform  or  nearly  uniform  manner  round 
the  whole  circumference.  The  magnetising  current  comes 
from  the  battery  B,  which  consists  preferably  of  three  or  four 
storage  cells ;  its  strength  is  regulated  by  the  adjustable 
resistance  E  and  is  measured  by  the  ampere-meter  G.  The 
reversing  key  K  has  its  terminals  e  and  d  connected  through 
an  adjustable  resistance  E2,  which  may  be  short  circuited  by 
the  key  S.  The  effect  is  that  when  S  is  closed  the  throwing 
over  of  the  reversing  key  simply  reverses  the  current  without 


FIG.  160.— Arrangement  for  Ballistic  Tests. 

altering  its  strength,  but  when  S  is  open  the  reversing  keynot 
only  reverses  the  current,  but  changes  its  strength  by  an  amount 
depending  on  the  value  of  B2.  This  device  is  required  in  taking 
cyclic  B-H  curves,  but  is  not  used  in  simple  tests  of  permea- 
bility;  and  if  the  arrangement  is  to  be  used  for  permeability  tests 
only  the  key  S  and  resistance  K2  may  be  dispensed  with,  and 
a  permanent  connection  is  then  made  between  e  and  d.  The 
two-way  key  C  allows  the  current  to  be  sent  either  into  the 
primary  coil  of  the  specimen  or  into  the  primary  coil  of  E, 
which  is  an  induction  coil  without  an  iron  core.  It  consists 


358  MAGNETISM  IN  IRON. 

of  a  primary  wound  on  a  brass  tube  or  other  non-magnetic 
core,  the  dimensions  of  which  are  carefully  measured,  and  in 
the  middle  of  the  length  a  short  secondary  coil  is  wound  over 
this,  which  is  permanently  connected  in  series  with  the 
secondary  coil  on  the  specimen  and  with  the  ballistic  galvano- 
meter Gr  The  function  of  E  is  to  serve  as  a  means  of 
standardising  the  ballistic  galvanometer.  From  the  known 
dimensions  and  winding  of  the  coils  it  is  easy  to  calculate  the 
number  of  lines  of  induction  which  cut  the  secondary  circuit 
when  a  given  current,  say  one  ampere,  is  reversed  in  the 
primary  of  E.  The  ballistic  effect  of  this  reversal  is  observed, 
and  in  this  way  it  is  ascertained  how  many  lines  of  induction 
correspond  to  one  scale  division  of  the  ballistic  galvanometer. 
In  calculating  the  induction  constant  for  the  coil  E  account 
must,  of  course,  be  taken  of  the  effect  of  the  ends.  A 
resistance  E3  in  the  secondary  circuit  allows  the  sensibility  of 
the  ballistic  galvanometer  to  be  regulated,  and  this  resistance 
must  be  made  sufficiently  great  to  prevent  a  too  rapid  damping 
of  the  swing.  The  author  prefers  a  galvanometer  of  the 
D'Arsonval  type  for  this  work :  its  period  is  readily  made 
long,  and  the  swinging  <?oil  is  quickly  brought  to  rest  by 
short-circuiting  it  through  the  key  F.  The  key  F  is,  in  fact, 
only  opened  to  allow  a  swing  of  the  galvanometer  to  be  read ; 
at  other  times  it  is  kept  closed.  Both  secondaries,  that  of 
the  specimen  A  and  that  of  the  standardising  coil  E,  are 
permanently  connected  in  series,  so  that  the  secondary 
circuit  undergoes  no  change  when  the  magnetising  current  is 
sent  into  E  for  standardising  or  into  A  for  testing. 

Simple  tests  of  permeability  are  made  by  reversing  the 
magnetising  current  and  observing  the  ballistic  effect  of  each 
reversal,  the  current  being  brought  to  a  number  of  successively 
increased  values  to  give  a  convenient  series  of  points  on  the 
B-H  curve.  After  adjusting  the  current  to  each  value,  the 
key  K  is  reversed  several  times  before  ballistic  readings  are 
taken,  in  order  to  escape  initial  effects.  The  induction  is 
calculated  from  half  the  ballistic  effect  observed  on  reversals 
of  the  magnetising  current.  In  these  tests  the  key  S  is 
kept  closed. 

When  a  cyclic  process  is  to  be  investigated  a  different 
procedure  is  followed.  The  current  is  brought  to  the  value 


OBTAINING    CYCLIC    CURVES.  359 

which  is  wanted  to  produce  the  extreme  induction  in  the 
cycle,  and  is  reversed  several  times  to  establish  a  cyclic  state. 
Then  it  is  suddenly  reduced  by  opening  the  short-circuiting 
key  S,  the  key  K  having  been  previously  put  over  to  the  left. 
The  effect  is  to  produce  a  step  from  the  highest  value  of  H,  at 
the  extremity  of  the  cycle,  to  a  value  which  is  less  high  by  an 
amount  depending  on  E2.  The  ballistic  effect  of  this  step  is 
observed ;  it  determines  the  amount  by  which  B  drops  in  this 
step -down  of  H  ;  S  is  then  closed,  and  the  key  K  is  reversed 
twice  or  oftener  to  re-establish  a  cyclic  state,  R2  is  set  to  a 
larger  value,  and  a  larger  step  is  similarly  made  by  again 
opening  S,  giving  another  point  on  the  cyclic  curve.  In  this 
way  as  many  points  are  found  as  will  determine  the  form  of 
the  curve  between  the  highest  value  of  H  and  the  value 
H  =  0.  Each  of  these  points  is  found  by  a  step  from  one 
extremity  of  the  cycle,  and  consequently  each  is  an  indepen- 
dent determination,  not  affected  by  any  error  that  may  have 
occurred  in  reading  other  steps.* 

To  continue  the  curve  we  have  to  determine  points  for 
which  H  is  negative.  This  is  done  by  using  the  reversing 
key  K  to  pass  from  the  full  positive  current  to  a  less  negative 
current.  After  reversing  the  full  current  several  times,  the 
key  is  switched  from  right  to  left  while  S  is  held  open, 
thereby  introducing  R0  as  well  as  reversing.  Repetition  of 
this  process  with  a  number  of  diminishing  values  of  B2  gives 
points  by  which  the  curve  is  extended  to  the  opposite  extremity 
of  the  cycle.  This  completes  the  test,  for  the  second  curve 
which  is  required  to  close  the  cycle  is  identical  in  form  with 
the  one  already  found.  The  further  operation  of  drawing  the 
cyclic  curve  and  measuring  the  enclosed  area  to  find  the 
hysteresis  loss  has  been  described  in  an  earlier  chapter. 

During  the  whole  determination  of  a  cycle  no  change  is 
made  in  the  resistance  R,  which  settles  the  maximum  of  H. 
When  one  cycle  is  completed  others  may,  of  course,  be  gone 
through  in  a  similar  way,  with  greater  or  less  magnetising 
current. 

The  process  is,  at  the  best,  somewhat  laborious,  but  with  a 
little  experience  in  selecting  suitable  points  on  the  curve  the 

*  The  advantage  of  operating  by  steps  from  an  extremity  of  the  cycle 
appears  to  have  been  first  pointed  out  by  Messrs.  Evershed  and  Vignoles. 


360 


MAGNETISM    IN    IRON. 


observations  need  not  take  long,  though  the  subsequen4 
reduction  of  them,  with  the  curve-plotting  and  measuring  of 
areas,  necessarily  takes  a  good  deal  of  time.  Fig.  161  is  an 
example  of  a  series  of  cyclic  curves  found  in  this  way,  in 
which  half  of  each  cycle  is  drawn  and  the  points  of  observa- 
tion are  marked  on  it.  It  will  be  noticed  that  the  curves 
of  each  cycle  in  general  overlap  slightly  the  rising  curve  of  a 
larger  cycle — a  feature  which  is  also  shown  in  cyclic  curves 
determined  by  the  magnetic  curve-tracer. 


4.0      U      U      13     <*     15     16 


FIG.    161. 


§  193.  Form  of  Specimens  for  Ballistic  Tests.— The  form 
to  be  preferred  is  that  of  a  closed  ring,  with  a  radial  width 
small  in  comparison  with  the  diameter.  It  has  been  explained 
in  §  57  that  this  condition  should  be  satisfied  in  order  to  make 
the  magnetising  force  approximately  uniform  over  the  cross - 
section.  In  testing  forgings  or  castings  the  ring  should  be 
turned  out  of  solid  metal,  and  in  testing  sheet  metal  it  is  best 
made  by  piling  up  a  number  of  flat  rings  stamped  out  of  the 
sheet.  To  make  a  ring  by  rolling  up  a  flat  strip  is  objection- 
able, for  the  specimen  is  then  subjected  to  conditions  of  stress 
different  from  those  which  apply  to  the  sheet,  though  this 
objection  may  be  partly  removed  by  annealing  the  ring  after 


BALLISTIC  TESTS   OP  RODS.  861 

it  is  formed.  The  size  of  the  ring  is  a  matter  of  convenience : 
about  10cm.  for  the  mean  diameter  and  1cm.  for  the  radial  width 
will  be  found  suitable,  and  this  is  large  enough  to  allow  the 
magnetising  coil  to  be  easily  wound  on.  The  cross-section  is  best 
ascertained  not  by  direct  measurement  (except  in  the  case  of 
very  carefully  turned  solid  rings),  but  by  finding  the  volume  of 
the  ring  and  measuring  its  mean  diameter,  the  volume  being 
found  by  weighing  the  ring  in  air  and  in  water.  With  rings 
piled  up  from  sheet  stampings  this  gives  a  much  more  accurate 
determination  of  the  average  section  than  can  be  arrived 
at  by  measuring  directly  the  thickness  of  the  separate  sheets. 

In  some  cases  it  may  be  necessary  to  test  the  material  in 
the  form  of  rods.  This  has,  for  instance,  to  be  done  where 
the  object  of  the  ballistic  test  is  to  ascertain  the  quality  of  a 
rod  which  will  serve  as  a  standard  of  comparison  in  tests  of 
the  kind  to  be  presently  described.  The  method  of  the  bar 
and  yoke,  described  in  §  59,  is  open  to  the  objection  that, 
with  a  very  permeable  material  such  as  forged  iron  or  dynamo- 
magnet  steel,  the  influence  of  the  yoke  is  too  great  to  be 
neglected,  and  there  is  no  means  of  eliminating  it  from  the 
results.  The  author  has  devised  a  method  in  which  two  bars 
and  yokes  are  used,  which  escapes  this  difficulty,  and  by  which 
the  permeability  of  iron  in  the  form  of  rods  may  be  determined 
very  exactly,  the  effect  of  the  yokes  being  eliminated  by  making 
two  tests  with  a  longer  and  shorter  length  of  the  same  pair  of 
bars  between  the  two  yokes. 

When  a  bar  is  reduced  to  endlessness  by  means  of  a  yoke, 
or  a  pair  of  parallel  bars  by  two  end  yokes,  a  distinction  must 
be  drawn  between  the  true  magnetising  force  H  and  the 
apparent  magnetising  force  (neglecting  the  yoke),  which  is 

~  times  the  number  of  ampere  turns  divided  by  the  clear  length 

of  the  bar  or  bars.  We  may  call  this  latter  force  H'.  Of  the 
whole  number  of  ampere  turns  in  the  magnetising  coil,  some 
are  used  in  overcoming  the  magnetic  reluctance  of  the  yoke  or 
yokes,  including  that  of  the  joints  between  yoke  and  bar,  and 
only  the  remainder  are  effective  in  magnetising  the  bar.  The 
use  of  a  pair  of  bars  with  two  yokes  allows  the  difference  to  be 
ascertained  between  the  apparent  magnetising  force  H'  and 
the  (smaller)  true  force  H. 


362 


MAGNETISM    IN    IRON. 


§  194.  Use  of  Double  Bars  and  Yokes. — Let  a  pair  of  equal 
bars  be  used,  united  at  their  ends  by  yokes  which  are 
preferably  made  as  short  and  as  permeable  as  possible 
(Fig.  162).  The  yokes  are  bored  so  that  the  bars  fit  them 
easily,  and  set-screws  at  the  sides  of  each  yoke  serve  to  clamp 
it  to  the  bars.  The  yokes  can  be  slid  nearer  to  each  other,  as 


FIG.  162. 

in  Fig.  163,  so  that  the  clear  length  of  bar  between  them  is 
reduced  to  half  its  original  value.  A  ballistic  test  is  made 
first  with  the  full  length,  and  then  with  the  half  length,  of 
clear  bar  between  the  yokes. 

Using  L  to  represent  the  whole  clear  length  of  the  bars 
between  the  yokes,  N  the  number  of  turns  in  the  magnetising 
coils,  and  C  the  current,  the  line  integral  of  magnetic  force  is 


This  is  partly  expended  in  producing  a  nearly  uniform  force 
H  in  the  bars,  and  partly  in  magnetising  the  yokes.     The 


FIG.  163. 

part  used  in  the  bar  is  HL.     If  we  call  the  part  used  in  the 
yokes  e,  we  have 


The  two  tests,  taken  together,  allow  us  to  find  c.     In  the  two 
tests  let  L!  and  L2  represent  the  clear  lengths,  and  let  Nj  and 


METHOD  OF  TWO  BARS  AND  YOKES.  363 

N2  represent  the  respective  number  of  turns  used  in  the 
magnetising  coils.  The  apparent  magnetising  force  in  the 
first  test  is 

u,     47I-CN, 
n  = — = — , 

and  in  the  second  test,  with  reduced  length,  it  is 

But  the  true  magnetising  force  H  is 

~LT~  ~I^ 

in  the  first  case,  and 


__ 

L2         L2 

in  the  second. 

Hence  H  =  H'-_- 

Li 

at  any  stage  in  the  first  test, 

and  H  =  H"-T- 

u* 

at  any  stage  in  the  second  test. 

Now  comparing  the  two  tests,  when  the  induction  B  has 
the  same  value  in  both,  the  true  magnetising  force  H  must  be 
the  same  in  both,  and  also  the  quantity  e  which  represents 
the  line  integral  of  the  force  in  the  yokes  must  be  the  same 
in  both. 

Hence,  for  equal  values  of  B  in  the  two  tests, 

Ht       £      1 1  ir      £ 
-  f-  =  rl  -=-, 

Ll  L2 

H'-H'  =  A-  €. 

L2     Lx 

In  this  result  there  is  no  assumption  as  to  the  ratio  of  L, 
to  L2.  Actually,  however,  we  make  L2  =  JL1,  and  in  that 
case  the  equation  becomes 

H"-H  =  * 
L, 

This  determines  -—  ,  and  by  subtracting  —  from  H'  we  find 

Li  Li 

the  true  force  H.      Having  drawn  from  the  two  tests  a  curve 


364 


MAGNETISM    IN    IRON. 


(1)  of  B  and  H',  and  (2)  of  B  and  H",  the  true  relation  of  B 
to  H  is  found  by  setting  back  a  curve  at  each  value  of  B  by 
the  distance  H"-  H'  from  the  curve  (1). 

An  example  will  help  to  make  the  method  clear.  For 
convenience  of  calculation  it  is  useful  to  take  the  length  Lx  as 
12-56cms.  and  the  length  L2  as  6-28cms.  Then,  if  coils  with 
100  and  50  turns  respectively  are  used,  the  apparent  magnet- 
ising forces  H'  and  H"  are  each  equal  to  10  units  per  ampere 
of  current.  This  was  the  case  in  the  following  example, 
which  refers  to  a  test  of  a  pair  of  Lowmoor  iron  bars  turned 
to  a  diameter  of  fin.  or  0-952cm.  The  yokes  were  rectangular 
iron  blocks,  2cm.  by  2 Jem.  in  section  and  2- 2cm.  from  centre 
to  centre  of  the  bars.  Ballistic  observations  were  made  as 
stated  in  the  table,  and  from  these  the  curves  of  Fig.  164 
were  drawn. 


I.  —  Bars  12'56cm.  long  between 

II.—  Bars  6'28cm.  long  between 

the  yokes. 

the  yokes. 

H'. 

B. 

H'. 

B. 

2-05 

1,650 

2-05 

1,360 

3-07 

4,600 

3-07 

3,160 

410 

7,440 

410 

5,660 

512 

9,460 

512 

7,920 

615 

10,750 

6-15 

9,560 

8-20 

12,280 

8-20 

11,590 

10-25 

13,200 

10-25 

12,700 

15-4 

14,410 

15-4 

14,160 

20-0 

14,950 

20-0 

14,750 

30-0 

15,700 

30-0 

15,550 

50-0 

16,550 

50-0 

16,470 

70-0 

17,160 

70-0 

17,050 

120-0 

18,100 

120-0 

17,960 

Fig.  164  shows  these  results  for  the  earlier  part  of  the 
curves  only.  The  abscissas  of  curve  (1)  are  the  values  of  H',  and 
those  of  curve  (2)  are  the  values  of  H".  The  curve  (3)  is  drawn 
by  reducing  the  abscissa)  of  curve  (1)  by  the  amount  H"-  H\ 

which  is  =-,     This  corrects  for  the  yokes,  and  gives  the  true 

relation  of  magnetising  force  to  induction  in  the  bars  them- 
selves. It  will  be  noticed  that  the  correction  for  the  yokes  is 
by  no  means  insignificantly  small,  even  with  such  short  yokes 
as  were  used  in  this  set  of  tests. 


METHOD  OP  TWO  BARS  AND  YOKES. 


365 


A  single  yoke,  such  as  that  shown  in  Fig.  27  (Chapter  III.), 
would  involve  a  still  larger  difference  between  the  real  and 
apparent  magnetising  forces,  and  the  amount  of  the  difference 
would  be  indeterminate.  The  advantage  of  the  double  yoke 
arrangement  is  that  the  difference  is  determined  and  allowed 
for,  with  the  effect  that  it  allows  rigorous  tests  to  be  made 
with  short  rods.* 


15000 
14000 
13000 
12000 
11000 
10000 
9000 
8000 
7000 
COOQ 
5000 
4000 
3000 
2000 
1000 


B 


0       1       2       3       4        5      6        7        8       9      10      11      12      13  15 

H  for  curve  (3),  H'  for  curve  (1),  H"  for  curve  (2). 
FIG.  164.  —  Method  of  Correcting  for  Yokes. 

The  use  of  two  bars  and  yokes  in  the  manner  here 
described,  involving  as  it  does  two  tests  with  the  yokes  at 
different  distances,  is  a  more  laborious  method  of  making 
ballistic  measurements  of  magnetic  quality  than  the  use  of  a 
turned  ring.  In  some  cases,  however,  specimens  may  have  to 
be  tested  in  the  form  of  rods,  and  it  is  then  that  the  method 
is  particularly  valuable.  Especially  is  this  the  case  when  the 
object  is  to  test  a  rod  which  will  serve  as  a  standard  in  the 
permeability  bridge  which  is  described  in  the  next  paragraph. 


See 


Nov.  20,  1896,  p.  110. 


MAGNETISM    IN    IRON. 


§  195.  Permeability  Bridge.— In  this  instrument  the  principle 
of  comparison  is  applied.     The  specimen  to  be  tested  is  in  the 


form  of  a  rod,  and  its  B-H  curve  is  obtained  by  finding,  at 
successive  degrees  of  magnetisation,  the  ratio  of  the  magnetising 


PERMEABILITY    BRIDGE.  367 

force  which  has  to  be  applied  to  the  specimen  to  that  force 
which  has  to  be  applied  to  a  standard  rod  in  order  that 
both  may  acquire  the  same  value  of  B.  Since  the  B-H 
curve  of  the  standard  rod  is  known  beforehand,  the  values 
of  this  ratio  suffice  to  determine  the  B-H  curve  of  the 
specimen  under  test.  The  process  of  comparing  the  two 
rods  is  immensely  less  laborious  than  that  of  making  an 
independent  set  of  ballistic  tests,  and  the  accuracy  of  the 
process  of  comparison  is  greater  than  the  acccuracy  likely  to 
be  reached  in  ballistic  tests.  As  carried  out  in  the  permea- 
bility bridge  the  process  lends  itself  well  to  workshop  tests. 

The  process  of  comparison  of  permeability  is  in  many  ways 
analogous  to  the  comparison  of  resistance  in  the  use  of 
Wheatstone's  bridge.  Mr.  Steinmetz  has  described  an  early 
apparatus  by  Eickemeyer  using  a  variable  standard,  and  the 
general  principle  has  also  found  applications  in  other  ways  by 
Mr.  Kennelly  and  Mr.  F.  Holden.*  In  the  author's 
apparatus,  shown  in  Fig.  165,f  the  magnetisation  of  the  rod 
under  test  is  adjusted  to  equality  with  that  of  the  standard  by 
varying  the  number  of  turns  in  the  magnetising  coil  on  one 
rod,  while  the  same  current  passes  in  series  through  the 
magnetising  coils  of  both.  The  equality  of  magnetism  in  the 
two  rods  is  adjusted  by  using  a  detector  which  exhibits  any 
inequality,  and  ceases  to  be  deflected  when  equality  is  secured. 

The  two  rods,  namely,  the  standard  whose  B-H  curve  is 
known  and  the  rod  to  be  tested,  are  slipped  into  two  parallel 
magnetising  coils,  and  their  ends  are  joined  by  two  short 
yokes  of  soft  iron.  In  Fig.  166  the  rods  are  shown  in  place 
between  the  yokes,  but  with  the  coils  removed.  In  Fig.  165 
the  yokes  appear  at  the  ends  of  the  brass  cover  which 
contains  the  two  coils.  From  the  yokes  two  long  iron 
horns  project  upwards,  which  nearly  meet  above,  and  in 
the  gap  between  these  a  box  containing  a  compass  needle 


*  Mr.  Holden's  apparatus  is  described  and  illustrated  in  an  article  by 
Messrs.  Parshall  and  Hobart  in  Engineering  for  January  7,  1898  (Vol. 
LXV.,  p.  2).  He  magnetises  the  two  bars  by  separate  currents,  the 
strength  of  which  is  adjusted  until  a  state  of  balance  is  arrived  at.  A 
magnetometer  above  the  bars  detects  the  leakage  of  magnetic  induction 
through  the  air  from  yoke  to  yoke  when  the  balance  is  imperfect. 

t  The  Electrician,  Vol.  XXXVII.,  p.  41. 


368 


MAGNETISM    IN    IRON. 


is  placed.  This  corresponds  to  the  galvanometer  of  a 
Wheatstone  bridge;  it  serves  as  a  detector  to  show  when 
the  two  yokes  are  at  the  same  magnetic  potential,  or,  in 


FIG.  166.— Bars,  Yokes  and  Horns  ;  cover  removed. 

other  words,  to  show  when  there  is  no  magnetic  induction 
across  from  yoke  to  yoke  through  the  two  iron  horns.  Such 
a  condition  will  be  produced  only  when  the  magnetic  induc- 
tion in  the  two  rods  is  the  same.  In  that  case  the  magnetic 


PERMEABILITY    BRIDGE.  869 

circuit  consisting  of  the  two  rods  and  the  yokes  will  be 
complete  in  itself.  The  lines  that  go  from  right  to  left  along 
one  rod  will  all  return  from  left  to  right  along  the  other. 
The  yokes  will  be  at  the  same  magnetic  potential ;  the  horns 
will  remain  unmagnetised,  and  the  detector  will  not  deflect. 
If  both  rods  have  the  same  permeability,  this  state  of  balance 
will  be  produced  by  having  the  same  number  of  ampere-turns 
act  on  each ;  but  if  they  differ  in  quality,  the  condition  of 
balance  can  still  be  produced  by  altering  the  relative  number 
of  ampere-turns.  To  do  this  the  number  of  effective  turns  in 
the  magnetising  coil  of  the  sample  bar  is  altered  by  means 
of  the  dial  switches,  while  the  same  current  passes  through 
both  coils. 

To  get  rid  of  all  effects  of  hysteresis  in  the  bars,  and  in  the 
yokes  and  horns,  a  reversing  key  (shown  on  the  right)  is 
worked  while  the  adjustment  proceeds,  and  the  balance  is 
perfect  when  each  reversal  produces  no  permanent  displace- 
ment of  the  compass  needle  between  the  horns.  A  transient 
kick  will  even  then  in  general  be  observed,  owing  to  a 
difference  in  the  time  rate  with  which  the  two  bars  take  up 
their  magnetism.  In  practice  the  adjustment  by  means  of 
the  dial  switches  is  very  readily  made,  and  takes  no  longer 
than  the  corresponding  process  in  measuring  resistances.  To 
prevent  the  current  from  altering  while  it  is  going  on,  the 
switches  are  furnished  with  a  second  set  of  contacts  which 
throw  in  compensating  resistances  as  the  number  of  turns  in 
the  magnetising  coil  is  reduced,  with  the  effect  that  the  total 
resistance  of  the  circuit  remains  unchanged.  The  clear  length 
of  each  bar  is  12*56cm.  (47r),  and  the  number  of  turns  in  the 
magnetising  coil  of  the  standard  bar  is  100.  Hence  the 
magnetising  force  due  to  its  coil  is  10  C.G.S.  units  for  each 
ampere  of  current.  This  allows  any  required  magnetising 
force  to  be  easily  applied,  with  the  aid  of  an  ampere-meter 
and  an  adjustable  resistance  outside  the  instrument.  Further, 
since  the  relation  of  B  to  H  is  known  for  the  standard  bar,  a 
knowledge  of  the  current  is  enough  to  show  at  what  value  of 
the  induction  B  the  comparison  is  being  made,  and  B  is,  of 
course,  the  same  for  both  bars  when  the  condition  of  balance 
is  produced.  The  number  of  turns  on  the  other  bar  then 
gives,  by  its  ratio  to  100,  the  ratio  of  the  magnetising  force 

PS 


370  MAGNETISM    IN    IRON. 

required  for  that  bar  to  the  known  force  applied  to  the 
standard.  Hence  a  point  in  the  B-H  curve  of  the  bar  under 
test  is  determined,  and  by  changing  the  current  as  many 
points  as  are  wished  may  be  found.  In  practice  it  is  conve- 
nient to  bring  the  current  to  a  value  such  as  1  ampere,  and 
then  increase  it  by  similar  steps,  thus  making  H  take  values 
of  10,  20,  &c.,  successively. 

The  same  method  of  comparison  applies  with  equal  facility 
to  earlier  stages  in  the  curve,  and  there  is  no  difficulty  in 
adjusting  the  balance  even  with  magnetising  forces  much 
weaker  than  10  units. 

The  detector  is  more  than  sensitive  enough  to  show  the 
effect  of  one  turn  more  or  fewer  in  the  magnetising  coil  when 
the  state  of  balance  is  approached,  and  might  even  be  used, 
by  interpolation  between  the  deflections  to  right  and  left,  to 
estimate  the  fraction  of  a  turn  necessary  for  exact  balance, 
although  in  practically  carrying  out  magnetic  tests  this  would 
be  superfluous.  The  sensitiveness  of  the  detector  needle  is 
regulated  by  an  adjustable  magnet  below  it. 

The  author  finds  that,  apart  from  its  great  convenience  over 
the  ballistic  method,  the  permeability  bridge  is  actually  a 
more  delicate  means  of  detecting  differences  between  one 
sample  and  another.  The  absolute  values  are,  of  course, 
dependent  on  the  primary  measurement  of  the  standard  bar, 
which  is  made  ballistically,  by  the  method  described  in  §  194. 

The  dial  switches  in  the  instrument  exhibited  give  the 
means  of  increasing  the  number  of  turns  on  the  test-piece  up 
to  210.  In  cases  where  the  test-piece  is  magnetically  much 
worse  than  the  standard,  a  ratio  of  rather  more  than  2  to  1 
may  be  insufficient ;  and  to  provide  for  that  there  is  a  two- 
way  arrangement,  by  which  the  number  of  turns  on  the 
standard  bar  is  readily  reduced  to  50,  when  H,  of  course, 
becomes  5  instead  of  10  per  ampere,  and  the  sample  under 
examination  can  then  have  more  than  four  times  as  much 
magnetising  force  as  the  standard  bar. 

When  it  is  desired  to  test  the  permeability  of  sheet  metal, 
the  samples  are  formed  by  piling  up  a  number  of  straight 
strips,  giving  a  total  cross-section  equal  to  that  of  the  standard, 
and  a  different  form  of  yokes  is  employed.  In  the  arrangement 
used  with  bars,  which  is  shown  in  Figs.  165  and  166,  the 


PERMEABILITY    BRIDGE. 


371 


attachment  of  the  bars  to  the  yokes  is  of  the  simplest  possible 
kind ;  the  bars  slip  through  holes  in  which  they  are  a  loose 
fit,  and  they  are  pressed  against  the  middle  portion  of  the 
yokes  by  a  pair  of  set  screws  outside.  The  effective  contact 
between  bar  and  yoke,  therefore,  is  made  in  the  place  best 
adapted  for  shortening  the  magnetic  circuit  through  the  yokes. 
In  the  instrument  shown  in  the  figures  the  bars  are  turned 
rods  fin.  in  diameter.  The  ends  do  not  have  to  be  faced. 

Fig.  167  illustrates  the  use  of  the  permeability  bridge. 
There  the  dotted  line  is  the  B-H  curve  of  the  standard  bar. 
The  full  line  is  the  curve  found  by  the  use  of  the  bridge  for 
a  particular  test  piece,  the  points  marked  on  it  being  the  actual 


16000 

14000 

12000 

10000 

8000 

60(0 

4000 

2000 


B 


H 


8       7       8 

FIG.  167. 


10   11   12   13   14  15 


points  of  observation.  In  this  case  the  current  was  adjusted 
to  a  series  of  values  such  as  to  produce  inductions  of  2,000, 
4,000,  6,000,  &c.,  and  comparison  was  made  at  each  of  these 
points.  For  example,  to  produce  an  induction  of  10,000  as  the 
standard  was  known  to  require  a  force  of  4-50  units.  The 
current  was  accordingly  adjusted  to  4-5  amperes.  It  was  then 
found  that,  with  100  turns  on  the  standard  bar,  127  turns 
were  needed  on  the  test-piece  to  secure  balance.  This  cor- 
responds to  a  force  of  * — ,  or  5*70,  which  determines 

the  point  marked  A  on  the  curve. 

An  important  practical  advantage  in  the  use  of  the  per- 
meability bridge  is  that  no  exact  adjustment  of  the  mag- 
netising current  is  necessary.  The  B-H  curve  of  the  bar  under 

B  B  2 


372 


MAGNETISM   IN   IRON. 


test  follows  much  the  same  general  course  as  the  curve 
of  the  standard  bar,  and  hence  the  ratio  of  magnetising  force 
for  the  two  is  not  much  changed  by  a  small  variation  in  the 
current.  It  follows  that  an  ordinary  commercial  ampere- 
meter gives  a  sufficiently  accurate  means  o  measuring  the 
current,  even  when  careful  comparison  of  the  test  bar  with  the 
standard  is  required. 

196.  Apparatus  using  a  Yoke  with  a  Gap. — In  several 
pieces  of   apparatus   designed  to  facilitate  magnetic  testing 


FIG.  168. 

in  the  workshop,  the  test  piece  takes  the  form  of  a  bar  whose 
magnetic  circuit  is  more  or  less  nearly  completed  by  means 
of  a  yoke,  but  a  gap  is  left  in  the  yoke  for  the  purpose  of 
measuring  there  the  induction  in  the  circuit  of  which  the  test- 
bar  forms  part. 

An  instrument  of  this  type  was  introduced  by  Koepsel  in 
1890,*  and  was  subsequently  improved  by  Kath.f  Figs.  168 

*  Verhandl.  Phys.  Gesellech.,  Berlin,  1890.  See  also  Du  Bois'  "  Magnetic 
Circuit,"  p.  331  ;  and  Elevtrotech.  Zeitschrift,  Vol.  XIII.,  1892  p.  560  ;  and 
Vol.  XV.,  p.  214. 

t  Mectrotech.  Zeitschrift,  1898,  p.  411. 


USE    OF    YOKE    WITH    GAP. 


373 


and  169  show  a  recent  form  (made  by  Siemens  and  Halske), 
Fig.  169  being  a  horizontal  section.  The  magnetic  circuit  of 
the  test  bar  P  is  completed  by  the  yoke  JJ  with  the  gap  h,  in 
which  a  small  coil  hangs  by  a  suspension  which  allows  the 
coil  to  turn.  The  bar  is  magnetised  by  a  coil  S,  to  which 
current  is  led  through  the  key  U.  An  auxiliai-y  current 
passes  at  h  into  the  suspended  coil,  and  causes  it  to  deflect  by 
an  amount  which  is  proportional  to  the  induction  in  the 
circuit,  for  a  constant  strength  of  auxiliary  current.  The 
deflection  of  the  coil  is  exhibited  by  means  of  a  pointer  on  a 
scale  attached  to  the  case,  which  is  removed  in  Fig.  168. 
Supplementary  magnetising  coils  are  wound  on  each  side  of 


the  yoke,  with  the  intention  of  compensating  for  that  part  of 
the  induction  in  the  circuit  which  is  due  to  other  causes  than 
the  permeability  of  the  test-bar. 

Other  methods  of  measuring  the  induction  in  the  gap  have 
been  resorted  to.  In  Bruger's  apparatus*  (made  by  Hartmann 
Braun)  this  is  done  by  inserting  a  spiral  of  bismuth 
wire,  which  has  the  property  of  altering  in  electrical 
resistance  in  a  magnetic  field  by  an  amount  depending  on  the 
strength  of  the  field.  Measurement  of  the  resistance  of  the 
bismuth  consequently  serves  as  a  means  of  determining  the 
amount  of  induction  across  the  gap.  This  method  has  the 
advantage  that  a-very  narrow  gap  suffices,  and  consequently 

*  Electrotech.  Zcitschrift,  1894,  Vol.  XV.,  p.  469. 


374  MAGNETISM    IN    IRON. 

the  shearing  over  of  the  apparent  B-H  curve,  which  any  gap 
causes,  may  be  made  less  in  this  apparatus  than  in  the  one 
just  mentioned. 

§  197  Du  Bois  Magnetic  Balance. — The  use  of  traction 
methods  in  magnetic  measurement  has  received  much 
attention  at  the  hands  of  Du  Bois,  whose  "  Magnetic 
Balance  "  (shown  in  Figs.  170  and  171)  presents  many  points 
of  interest.  In  the  more  primitive  appliances  for  testing  by 
means  of  traction  (§  148)  the  pull  on  a  section  of  the 


FIG.  170. 

magnetised  test-piece  itself  is  the  force  which  is  measured : 
Dr.  du  Bois  avoids  this  by  measuring  the  tractive  force  across 
a  gap  in  the  yoke  which  completes  the  magnetic  circuit  of 
which  the  test-piece  forms  part.  The  test-piece  is  a  rod, 
turned  for  convenience  to  a  diameter  of  1 '128cm.  in  order 
that  its  cross-sections  may  be  1  sq.  cm.  Its  clear  length 
between  the  two  arms  of  the  yoke  is  4?r  cm.  The  magnetic 
circuit  is  completed  by  a  piece  YY  capable  of  rocking  011  a 
knife  edge  at  E,  and  carrying  a  scale-beam  on  which  the 
weights  WW  slide.  In  rocking  to  the  left  Y  comes  against  a 
stop  at  I,  and  by  adjusting  the  sliding  weight  it  is  pulled 


DU    BOIS'    MAGNETIC    BALANCE. 


375 


away  from  this  stop ;  the  position  of  the  weight  is  then  read 
on  the  scale.  The  equilibrium  of  the  piece  Y  is  unstable,  but 
a  definite  reading  is  obtained  of  the  force  required  to  make  it 
rock  over  from  contact  with  the  stop  at  I.  From  this  force 
the  value  of  B  is  inferred,  and  the  magnetising  current  gives 
an  apparent  H  which  has  to  be  corrected  for  the  yoke  and 
air-gap  to  find  the  true  H  acting  on  the  bar.  Dr.  du  Bois 
provides  a  ready  means  of  making  this  correction  by  supplying 
with  the  instrument  a  curve  showing  to  what  extent  the 
apparent  B-H  curve  has  to  be  sheared  back  to  give  the  true 


^ 


02030   40     SO       60        70         ,.80  SO  JOO     """"-,- 


FIG.  171 


B-H  curve.  This  curve  is  definite  for  any  one  instrument, 
so  long  as  the  magnetic  quality  of  the  yoke  and  the  width  of 
the  air  gap  remain  unchanged.  Its  form  is  determined  in  the 
first  ID  stance  by  testing  a  bar  whose  magnetic  quality  is  known 
beforehand.* 

§  198.  The  Author's  Magnetic  Balance. — A  simple  form -of 
magnetic  balance  has  been  devised  by  the  author  with  the 
object  of  finding  expeditiously  the  value  of  B  corresponding 
to  a  single  value  of  H.  The  value  of  H  chosen  for  this  test 

*  Du  Bois,  "  The  Magnetic  Circuit  in  Theory  and  Practice,"  p.  346,  The 
Electrician,  August  26,  1892.,  Vol.  XXIX.,  p.  448. 


376  MAGNETISM    IN    IRON. 

is  20  C.G.S.  units.  A  determination  of  the  induction  pro- 
duced by  this  force  suffices  to  give  a  good  general  idea  of 
the  merit,  in  point  of  permeability,  of  forgings  or  steel  cast- 
ings intended  for  use  in  dynamo  magnets.  For  many  purposes 
it  is  unnecessary  to  determine  the  B-H  curve  as  a  whole  ;  a 
single  point  for  a  sufficiently  high  force  is  enough  to  show 
whether  the  specimen  is  permeable  and  how  it  compares 
with  other  specimens.  This  is  because  the  general  trend 
of  the  B-H  curve  in  material  of  the  classes  named  does  not 
vary  much  from  one  specimen  to  another  :  though  the  curves 
of  different  specimens  often  cross  each  other  in  the  early 
stages,  when  H  is  small,  they  seldom  do  so  when  H  is  fairly 
large.  If  a  piece  is  good  when  H  =  20,  it  remains  good 
under  stronger  forces,  and  a  specimen  which  has  relatively  low 
permeability  under  this  force  does  not  take  a  better  place 
when  the  force  is  increased — at  least  within  the  limits  that 
hold  in  ordinary  use.  A  force  of  20  C.G.S.  units  is  selected 
for  the  purpose  of  this  test  as  being,  on  one  hand,  sufficiently 
low  to  make  the  distinction  wide  between  good  and  bad  speci- 
mens, and,  on  the  other  hand,  sufficiently  high  to  make  the 
order  of  merit  substantially  the  same  as  the  specimens  main- 
tain when  they  are  subjected  to  any  strong  forces. 

The  author's  balance  is  shown  in  Fig.  172.*  The  tractive 
force  which  it  measures  is  that  which  is  excited  between  the 
side  of  the  magnetic  rod  and  a  suitable  pole-piece  :  hence  no 
facing  of  the  end  of  the  rod  is  necessary.  The  rod  is  a  turned 
bar  Jin.  in  diameter  and  4in.  long.  It  rests  horizontally  on 

the    two  poles  of  a  I 1  shaped  electro  magnet,  which    is 

excited  by  a  constant  current  of  such  strength  as  to 
produce  a  magnetising  force  in  the  rod  of  about  20  C.G.S. 
units.  In  one  of  the  poles  there  is  a  V-shaped  notch 
for  the  bar  to  rest  in,  and  the  other  pole  has  a  slightly 
convex  surface,  so  that  the  side  of  the  rod  touches  it 
at  one  point  only.  The  rod  requires  no  preparation 
beyond  turning  to  the  proper  diameter :  its  cylindrically- 
turned  side  touches  the  convex  pole  piece  in  a  perfectly 
definite  manner  so  long  as  it  is  free  from  rust  and  dust,  and  it 
may  be  removed  and  replaced  without  altering  the  character 
of  the  contact.  To  measure  the  tractive  force  at  this  point 
*  Jour.  lust.  Llect.  Bug.,  May  12,  1898. 


EWING  S    MAGNETIC    BALANCE. 


377 


of  contact  a  lever  or  weigb-beam  is  used,  wbicb  pulls  the  rod 
away  from  the  convex  pole,  while  the  other  end  of  the  rod 
remains  in  the  V  notch  in  the  other  pole,  forming  with  it 
what  may  be  called  a  magnetic  hinge.  The  tractive  force  is 
measured  by  means  of  a  weight  which  slides  along  a  graduated 
scale  on  the  weigh- beam.  When  the  rod  is  put  in  place,  in 
contact  with  the  pole,  the  current  is  reversed  once  or  twice  to 
wipe  out  any  effect  of  previous  magnetisation.  The  sliding 
weight  is  then  moved  along  the  beam  until  the  beam  just 
drops  every  time  it  is  raised  to  bring  the  rod  into  contact  with 
the  pole. 

The  scale  of  the  weigh-beam  is  a  linear  onp,  in  which  equal 
divisions  correspond  to  equal  differences  in  B,  for  a  constant 


FIG.  172. 


value  of  H.  It  is  graduated  to  give  by  direct  reading  the 
value  of  B,  for  H  =  20.  This  uniform  graduation  is  arrived 
at  in  consequence  of  the  fact  that  with  different  specimens  the 
magnetising  force  is  not  quite  constant,  although  the  current 
in  the  electromagnet  is  constant.  A  specimen  of  high 
permeability  increases  the  induction  in  the  magnetic  circuit, 
and  consequently  causes  a  larger  share  of  the  magneto- 
motive force  to  be  used  in  that  portion  of  the  circuit 
which  lies  outside  of  the  specimen  itself.  Hence  the  induction 
in  the  specimen  is  less  high  than  its  greater  permeability 
would  imply  ;  in  other  words,  the  better  specimen  is  exposed 
to  a  somewhat  less  magnetising  force  than  the  worse  specimen 
is  exposed  to.  The  tractive  force  increases  more  rapidly 
than  in  simple  proportion  to  the  actual  induction ;  but 


378  MAGNETISM    IN    IRON. 

matters  are  so  arranged  that  the  lessening  of  the  induction 
which  comes  about  in  the  way  just  stated  compensates  for 
this,  and  the  observed  differences  of  tractive  force,  as  mea- 
sured throughout  the  range  of  the  scale,  stand  in  simple 
proportion  to  the  differences  in  the  values  of  B  which  the 
various  specimens  would  exhibit  if  the  force  H  were  con- 
stant. In  other  words,  a  scale  of  equal  parts  on  the  weigh- 
beam  corresponds  to  equal  differences  of  B  under  a  constant 
magnetising  force,  and  the  weigh-beam  is  accordingly  lettered 
to  read  B  directly  in  equal  divisions.  The  readings  give  B 
for  H  =  20,  although,  in  consequence  of  the  action  just 
explained,  the  actual  magnetising  force  is  barely  20  for  rods 
of  very  good  quality,  and  somewhat  exceeds  20  for  rods  of 
lesser  permeability.  The  scale  is  adjusted  by  the  maker  by 
selecting  values  of  the  sliding  weight  and  of  a  fixed  weight  on 
the  weigh-beam  which  will  bring  the  readings  into  agree- 
ment with  the  known  values  of  B  in  certain  standard  rods. 

A  single  standard  rod  is  supplied  with  each  instrument,  and 
the  observer  adjusts  his  current  until  the  tractive  force  on 
that  rod  is  such  that  the  sliding  weight  stands  at  the  place  on 
the  beam  corresponding  to  the  known  value  of  B  which  a 
force  of  20  C.G.S.  units  produces  in  that  standard.  The 
standard  rod  consequently  serves  instead  of  an  ampere  gauge, 
and  no  other  current-measurer  is  required.  A  rheostat  is 
provided  in  the  instrument  for  regulating  the  current,  and  a 
single  small  storage  cell  forms  the  necessary  battery.  The 
observer  puts  in  the  standard  rod  and  turns  the  rheostat 
until  he  finds  that  the  weigh-beam  just  drops  each  time  it  is 
lifted,  while  the  sliding  weight  indicates  the  known  value  of 
B.  He  then  puts  in  tbe  rod  which  is  to  be  tested,  and  finds 
the  position  which  the  sliding  weight  has  to  take  for  it,  no 
change  being  made  in  the  current. 

§  199.  Hysteresis  Tester. — For  the  purpose  of  carrying  out 
commercial  tests  of  sheet-iron  for  hysteresis  in  a  more  expe- 
ditious and  simpler  manner  than  by  determining  the  form  of 
the  B-H  cycle,  recourse  has  been  had  to  the  direct  measure- 
ment of  the  work  expended  in  causing  a  test-piece  to  revolve 
between  the  pole  of  a  magnet,  or  in  causing  the  magnet  to 
revolve  while  the  test-piece  remains  at  rest.  In  an  apparatus 


HYSTERESIS    TESTER.  379 

of  this  class  designed  and  used  by  Mr.  F.  Holden*  the  speci- 
men was  a  ring  of  sheet  stampings  such  as  would  be  used  in 
a  ballistic  test.  It  was  supported  on  a  vertical  axis,  round 
which  a  field-magnet  was  caused  to  rotate.  In  consequence 
of  hysteresis  the  ring  tended  to  follow  the  magnet  poles  in 
their  rotation.  The  amount  of  this  tendency  was  measured 
by  a  helical  spring,  which  prevented  the  specimen  from 
turning,  the  ring  being  brought  to  its  initial  position  by 
means  of  a  torsion  head  furnished  with  a  scale.  For  a  given 
induction  the  readings  of  the  torsion  head  give  a  measure  of 
the  hysteresis. 

In  the  author's  hysteresis  tester!  the  specimen  is  made  up 
in  the  form  of  a  small  bundle  of  rectangular  strips,  fin.  wide 
and  Sin.  long.  This  is  supported  on  a  carrier,  which  is  made 
to  revolve  about  a  horizontal  axis  between  the  poles  of  a 
C-shaped  permanent  magnet,  which  is  carried  on  knife  edges, 
giving  it  freedom  to  swing  about  the  same  horizontal  axis  as 
that  about  which  the  specimen  revolves.  The  lower  side  of 
the  magnet  is  weighted  to  give  it  some  stability,  and  accord- 
ingly it  becomes  deflected  when  the  specimen  revolves  by  an 
amount  which  depends  on  the  hysteresis.  This  deflection  is 
read  by  means  of  a  long  pointer  and  a  scale  above.  The 
instrument  is  shown  in  Fig.  173.  A  vane  fixed  at  the  bottom 
of  the  magnet,  and  working  in  a  box  below  filled  with  oil,  acts 
as  a  dash-pot  to  prevent  swinging. 

The  deflection  of  the  pointer  shows  how  much  work  is 
expended  in  each  revolution  of  the  specimen  in  consequence 
of  hysteresis  in  the  induction  of  magnetism  between  it  and  the 
magnet.  A  definite  amount  of  work  is  done  in  each  revo- 
lution, whatever  the  frequency,  and  consequently  the  deflection 
of  the  magnet  is  independent  of  the  speed  at  which  the  carrier 
revolves,  provided  the  rate  is  not  so  high  as  to  produce  a 
fanning  action  in  the  air,  or  to  affect  the  result  through 
the  influence  of  Foucault  currents.  If  the  carrier  is  turned 
very  slowly,  the  magnet  shows  the  individual  impulses  it  receives 

*  Electrical  World,  June  15,  1895.  The  apparatus  is  described  and 
illustrated  by  Messrs.  Parshall  and  Hobart  in  Engineering,  Jan.  14,  1898, 
Vol.  LXV.,  p.  42. 

f  Jour.  Inst.  Elect.  Eng.,  April  25,  1895- 


380 


MAGNETISM    IN    IRON. 


as  the  ends  of  the  specimen  pass  its  poles ;  if  the  rate  is 
sufficiently  quickened  these  impulses  blend  into  a  steady 
deflection,  and  the  speed  may  be  considerably  increased  beyond 
this  without  making  the  deflection  change.  Hence  no  parti- 
cular care  to  keep  the  speed  of  rotation  uniform  is  required. 
In  using  the  instrument  the  operator  inserts  the  sample,  and 


FIG.  173. 

secures  it  in  the  carrier  by  clamps,  then  begins  to  turn  the 
handle,  and  lets  the  magnet  down  on  its  knife  edge.  After 
reading  the  deflection  to  one  side  he  reverses  the  direction  of 
rotation  and  reads  the  deflection  to  the  other  side,  The 
mean  of  the  two  readings  is  taken  as  the  true  deflection.  To 
allow  the  readings  to  be  interpreted  in  absolute  measure,  two 
standard  samples,  the  hysteresis  of  which  is  known,  are 


HYSTERESIS    TESTER.  381 

furnished,  and  the  deflections  given  by  them  are  observed  at 
the  time  when  tests  are  made. 

The  magnet  is  of  such  strength  as  to  produce  in  the 
specimen  an  induction  B  of  about  4,000  units,  and  the 
numerical  statements  of  the  hysteresis  are  referred  to  this  value 
of  B.  But  as  the  whole  action  is  one  of  comparison  between 
the  test  pieces  and  the  standards,  the  exact  strength  of  the 
magnet  field  is  a  matter  of  indifference;  and  if  the  magnet 
lose  some  of  its  strength  after  a  time,  the  accuracy  of  the 
comparison  is  not  affected,  since  the  ratio  of  hysteresis  loss 
between  two  samples  remains  the  same  or  very  nearly  the 
same  at  various  inductions,  as  Mr.  Steinmetz's  formula 
requires. 

The  deflection  varies  as  the  hysteresis  loss  plus  a  constant. 
If  a  sample  could  be  found  without  hysteresis  it  would  still 
produce  some  deflection,  because  its  rotation  would  cause  the 
magnet  poles  themselves  to  undergo  periodic  variation  in  the 
distribution  of  their  magnetism,  and  the  hysteresis  involved 
in  these  magnetic  changes  would  show  itself  as  work  spent, 
and  would  consequently  produce  a  deflection  ;  hence  the  con- 
stant in  the  relation  of  deflection  to  hysteresis  in  actual 
specimens.  To  interpret  the  results  the  most  convenient 
method  is  to  observe  the  deflections  dl  and  d.2  given  by  the 
two  standards  whose  known  hysteresis  losses  at  B  =  4,000  are 
Wx  and  W2.  Then  plot  di  and  d2  against  Wj  and  W2  on 
squared  paper,  and  draw  a  straight  line  through  the  two 
points  thus  found.  This  line  gives  the  amount  of  hysteresis 
corresponding  to  any  deflection. 

The  author  found  that  the  thickness  of  the  bundle  of  strips 
composing  the  test  piece  might  be  changed  considerably  with- 
out changing  the  deflection ;  hence  no  exact  adjustment  of 
thickness  is  required,  but  in  each  specimen  that  number  of 
strips  is  used  which  will  give  a  thickness  most  nearly  equal  to 
that  of  the  standards. 

In  apparatus  of  this  class,  where  readings  are  interpreted 
by  comparison  with  standards,  the  result  depends  on  the 
constancy  of  the  standards.  The  hysteresis  of  iron  cannot  be 
relied  on  to  remain  absolutely  unchanged  with  lapse  of  time, 
even  at  atmospheric  temperatures.  lu  some  specimens  no 
change  is  detected ;  others  apparently  alter  very  slowly. 


382  MAGNETISM    IN    FRON. 

Though  no  large  changes  take  place  in  any  case,  it  is  desirable 
to  have  the  standards  themselves  tested  from  time  to  time 
by  comparison  with  pieces  whose  magnetic  quality  is  freshly 
determined  by  ballistic  tests. 

The  hysteresis  loss  in  the  standards  is  stated  in  ergs  per 
cubic  centimetre  per  cycle  for  B  =  3 ,000,  and  also  in  watts  per 
Ib.  f(-r  a  frequency  of  100  for  cycles  with  the  same  limits 
of  B,  the  latter  number  being  deduced  from  the  former  by 
multiplying  by  0-000589.  If  the  formula  of  Mr.  Steiametz 
be  held  to  apply,  which  makes  the  hysteresis  equal  to  77  B1'6, 
corresponding  values  of  the  coefficient  77  are  found  by  dividing 
the  loss  in  ergs  by  580,000,  or  the  loss  in  watts  per  Ib. 
by  341. 


INDEX      TO      CONTENTS, 


INDEX. 


PAGE 

JEolotropy  (Magnetic)  due  to  Stress       232,244 

Ageing  of  Iron  by  Prolonged  Exposure  to  Heat  ...         ...  193 

Air-Gap  Equivalent  to  a  Joint,  Calculation  of  the  Thickness  of       ...     287 
„      in  a  Ring,  Magnetic  Resistance  of  ...         ...         ...  275 

„       Graphic  Representation  of  the  Influence  of 278 

Ampere's  Hypothesis  regarding  Magnetic  Molecules         ...         ...  352 

Annealing,  Influence  of,  on  the  Magnetic  Quality  of  Iron  and  Steel...       82 

Axis,  Magnetic 2 

Baily  (F.),  on  Hysteresis  in  Rotation 327 

Ballistic  Galvanometer  ...         ...         ...         ...         ...         ...  59 

Calibration  of 60,62,63 

„  „  Damping  of 63 

„      Method  36,59,356 

„  „        Example  of          ...         ...         ...         ...         ...  70 

„       Tests  of  Rings  and  Rods  64,360 

Bar  and  Yoke  67,361 

„  „      considered  as  a  Magnetic  Circuit  271,362 

Barrett  (W.  F.) :  Discovery  of  Recalescence          167 

„  on  Strains  caused  by  Magnetisation...         ...         ...     249 

Barus  and  Strouhal 83 

Baur,  Effects  of  Temperature      166,169 

„      Experiments  with  Weak  Magnetic  Forces 125 

Beattie  and  Clinker          328 

Becquerel  (E.),  on  Effects  of  Torsion  331 

Beetz  :  Experiment  bearing  on  Molecular  Theory       ...         ...         ....     296 

Bid  well  (S.) :  Change  of  Dimensions  due  to  Magnetisation         ...  224 

„  Experiments  on  Tractive  Force ...         ...         ...         255,259 

„  „  with  Strong  Magnetic  Forces  ..         ...  137 

Bosanquet:  Experiments  with  Iron  and  Steel  Rings  ...         ...         ....     137 

„  „  on  Tractive  Force          ...         ...         ...  256 

,,  „  Magnetomotive  Force         265 

Bruger ...         373 

Capstick(J.W.) « 350 

OC 


386  INDEX. 

PAGK 

Cast  Iron,  Curve  of  Magnetisation  of          85 

Chree  :  Influence  of  Pressure  on  the  Magnetic  Qualities  of  Cobalt    92.  223 

Chrome  Steel 83 

Circuit,  Magnetic ,         ...         262 

„        „  Equation  of          268 

Circular  Magnetism  produced  by  Twist  237 

Classification  of  Methods  in  Magnetic  Measurements        ...         ...  36 

Cobalt,  Curves  of  Permeability  92 

„       Effects  of  Stress  in „         222 

„       Experiments  with  ... 88,153 

Coefficients  of  Leakage  ...          283 

Coercive  Force       52,77 

Cohn  (E.)  :  Hysteresis  in  Effects  of  Stress  230 

Compensating  Coil  42,48,57 

„  Magnet,  use  of  ;..         56 

Compression  Apparatus    ...         ...         ...         ...         ...         203 

„  Influence  of,  on  the  Magnetic  Eesistauce  of  Joints  289 

Compressive  Stress,  Effects  of,  in  Nickel  202 

Concentration  of  Magnetic  Field  by  Cones  „..         145 

Conduction,  Electric  Analogy  of  Induced  Magnetism  to         ....  22,  265 

Cowan  (G.  C.) :  Experiments  on  Effects  of  Stress  in  Nickel        ...  199 

Creeping,  Magnetic  ...         ...         ...     128 

Critical  Temperature  ...         ...         ...         ...  166 

„  „  Change  of  Physical  State  at      167 

„       Temperatures  in  Nickel  Iron  Alloys  ...         ...         ...  186 

Curve  Tracer          ...     118 

Curves  of  Magnetisation         ...         ...  52 

„  „  for  Soft  and  Hard  Iron         81 

,,  Permeability  and  Susceptibility  ...         ...         ...  88 

Cyclic  Process  in  a  Group  of  Pivoted  Magnets  ...         ...         ...     351 

„  „        Repetitions  of  338 

)t  J        of  Magnetisation  ...       75 

„  „  Heating  Effect  of 102 

„      Regime,  Establishment  of  338,347 

, ,       Stress,  Effects  of,  in  Nickel 206 

„  Iron  216 

Demagnetising  by  Reversals 46 

Diamagnetic  Substances 16 

Differential  Susceptibility  and  Permeability  56 

Directing  Force  on  Magnetometer,  Measurement  of 47 

Dissipation  of  Energy  through  Magnetic  Hysteresis         99,  326 

Double  Bars  and  Yokes 362 

Du  Bois  :  Critical  Temperature  of  Nickel 178 

„          Experiments  with  Ellipsoids  ...         ...         ....         .-     163 

„  „     Magnetite      16S 

Jf  „  „     Strong  Magnetic  Forces  ...         138, 15cJ 

„        on  Split-Ring  Magnets       276 

Du  Bois' Magnetic  Balance          374 


INDEX.  387 

PAGE 

Dynamos,  Magnetic  Circuit  in     ...         ...         ...         ...         ...         ...     282 

Earth  Coil,  Use  of,  in  Ballistic  Method        .„          60 

Earth's  Field,  Elimination  of      ...         ...         ...         ...         ...         ...       46 

Elasticity  of  Metals,  Imperfect         231 

Ellipsoid,  Magnetisation  of          ...         ...         ...         ...         ...         ...       23 

„         Self-Demagnetising  Force  in       ..,         ...          34,279 

Ellipsoids,  Experiments  with  (Dubois)  ...         ...         ...         ...         ...     165 

Endlessness,  Condition  of      ...         ...         ...         ...         ...         ...  35 

Ends  of  a  Rod,  Influence  of         21 

Energy  Dissi  pated  in  Magnetisation 99 

E ver shed  and .Vignoles      ...         ...         ...         ...         ...         ...         ...     359 

Ewing  and  Cowan        ...         ...         ...         ...         •••         •••         •••  199 

EwingandLow     ...         137,143,285 

Ewing  :  Experimental  Researches  in  Magnetism        70,  76,  82,  94,  99,  105, 

114,  128,  181,  209,  217,  225,  237,  316 
„         Magnetic  Curve  Tracer       ...         ...         ...         ...         ...  118 

„         Magnetic  Qualities  of  Iron        ...         ...         ...         ...         ...     123 

„        Model  of  Molecular  Magnets  348 

„        Molecular  Theory  of  Magnetisation     ...         ...         ...         ...     299 

Swing's  Hysteresis  Tester 379 

„        Magnetic  Balance  ...          ...         ...         ...         ...         ...     375 

„        Method  of  Double  Bars  and  Yokes  362 

„        Permeability  Bridge       ...         ...         ...         ...         ...         ...     366 

Faraday 15,160 

Field,  Magnetic      ...         ...         ...         ...         ...         ...         ...         ...         3 

„  „       due  to  a  Solenoid      ...         ...         ...         ...         ...  6 

„     Uniiorm       ...         ...         ...         ...         ...         ...         ...         ...         6 

Finzi(G.)         330 

Fleming  (Prof.  J.  A.)        112 

Flux,  Magnetic  ...         ...         ...         ...         ...         ...         ...  263 

Force,  Magnetic     ...         ...         ...         ...         ...         ...         ...        3,11,12 

,.  „          Line  Integral  of      ...          ...         ...         ...         ...  265 

Form  of  Bodies,  Influence  of        ...         ...         ...         ...         ...         ...       28 

Free  Magnetism  ...         ...         ...         ...         ...         ...         ...  2 

„  „          of  an  Ellipsoid 26 

Frohlich's  Formula 333 

Fromme(C.)          138,339 

Gerosa(G.  G.) 330 

Glazebrook  (R.  T.)  352 

Gore  :  Change  in  Length  of  Iron  and  Steel  at  Critical  Temperature      167 
Graded  Cyclic  Magnetisation  of  Iron     ...         ...         ...         ...         ...     106 

„  Steel  108 

Graphic  Process  of  Allowing  for  the  Self -Demagnetising  Force        ...       54 
»  ,,        „  Treating  Air  Gaps         ...         .„         ...         ...  278 

„         Treatment  of  the  Magnetic  Circuit 280 

Gray  (A.)          47 

Hadfield's  Manganese  Steel          85 

»  ,,  in  Strong  Fields         ...         ...         ...  153 


INDEX. 

PAGE! 

Haubner(J.)          138 

Heat  Generated  in  a  Cyclic  Process  of  Magnetisation       ...         ...  102 

Holden,  F. 367,379 

Honig  :  Experiments  on  Heating  Effects  of  Magnetic  Reversals  110 

Hoopes  (A.) :  Experiments  on  the  Molecular  Theory       ^50 

Hopkinson  and  Wilson      123 

Hopkinson  (J.) 54,99 

„  Experiments  on  Effects  of  Temperature          ...         166.170 

„  „  „  Nickel-Iron  Alloys  186 

„  „  with  Various  Steels        ...         85,  88,  104,  153 

„  Heat  Liberated  in  Recalescence       ...         168 

Method  of  Bar  and  Yoke  67,  69,  79,  284 

„  on  Residual  Magnetism  in  Ellipsoids          ...         ...  289 

Hopkinson  (J.  and  E.)  on  the  Magnetic  Circuit  263 

Hughes  (D.  E.)  on  Effects  of  Twist 240 

Hysteresis 93,238 

„          Dissipation  of  Energy  through 99,107,326 

„          in  Recalescence  ...         ...         ...         180 

„          in  relation  to  the  Molecular  Theory      327 

„          in  the  Effects  of  Stress         ..     213 

„          in  a  Rotating  Field         326 

„          in  Transformer  Cores  ., 193 

„          in  Reduction  of,  by  Vibration 113,  232,  329 

„          in  the  Molecular  Configuration  of  Unmagnetised   Iron 

225,  227,  230,  347 

„          Steinmetz  Coefficient  of        Ill 

Imperfect  Magnetic  Circuit 264,273 

Induction,  Magnetic         12 

„       Tubes  of  263 

Instability  of  Molecular  Groups ...         ...         ...         ...         ...         ...     301 

Intensity  of  Magnetisation ...         ...         ...  7 

„        „  „  Limit  of       ...         ...         52 

Internal  Stress  due  to  Magnetisation          ..,         255 

Iron,  Curves  of  Susceptibility  of ...         ...         ...       90 

,,    Effects  of  Stress  in        209 

„    Test  of,  by  the Magnetometric  Method    ...         ...         ...         ...      49 

„    (Wrought)  Curves  of  Magnetisation  of  53,  72,  75,  76,  78,  81,  90,  95, 
96,  106,  114,  169,  177,  185,  210,  213,  229 

Isthmus  Method          138 

„  „       Apparatus  for 156 

„  „      Experiments  with  ., 138, 150 

„      Theory  of         145 

Joints,  Magnetic  Resistance  of          285,291 

Jones  (E.  Taylor) 254,256,260 

Joule:  Experiments  on  Tractive  Force       ...          255 

„        on  Strain  caused  by  Magnetisation       ...         249 

Kapp  (G.)  on  the  Magnetic  Circuit  of  Dynamos ...  263 

r        Dissipation  of  Energy  through  Hysteresis 107 


INDEX.  389 

PAGE 

Kapp(G.) :  Experiments  with  Strong  Magnetic  Forces         ...         138,  156 

Kath      372 

Kelvin  (Lord)         15,16,41,59,62 

„          „      Investigation  of  Effects  of  Stress      ...         197,222,231,234 

Kennelly  (J.  A.)      112,367 

Kerr's  Constant          ...         ...         ...         ...         ...         ...         ...  159 

,,       Discovery  of  Magneto -Optic  Rotation    ...         ...         ...         ...     158 

Klaassen  (Miss  H.  G.) :  Experiments  on  Groups  of  Magnets       ...  351 

„  „  „  „   Hysteresis      112,  123 

Knott(C.  G.) 56 

„          „        on  Effects  of  Superposed  Magnetisms 236 

Koepsel 372 

Kohlrausch(W.) 167 

Lamont-Frohlich  Formula     ...         ...         ...         ...         ...         ...  333 

Leakage,  Coefficients  of 283 

Length,  Influence  of,  in  the  Magnetisation  of  Hods          .,.         ....  77 

Line-Integral  of  Magnetic  Force 265 

Lines  of  Force ...         ...         ...         ...         ...         ...         ...         ...  5 

„       Magnetic  Induction        ...  ..         ...         ...         ...  12,13 

„       Magnetisation  ...         ...         ...         ...         ...         ...  9 

Long  Rod,  Magnetisation  of        ...         ...         ...         ...         ...         ...       30 

Lowmoor  Wrought  Iron  under  Strong  Magnetic  Forces 142 

Low  (W.) :  Experiments  on  Cobalt       92,233 

„  „          with  Strong  Magnetic  Forces 138,156 

„  Magnetic  Resistance  of  Joints         ...         ...         ...         ...     285 

Magnetic  JEolotropy  produced  by  Stress     ...         ...         ...         ...          233 

„       Analogy  of,  to  Electric  Conduction  ...         ...         ...         ...       22 

„       Axis 3 

Magnetic  Balance 374,375 

„       Circuit         262,268 

„  „      Graphic  Treatment  of 280 

„       Curve  Tracer          118 

„       Field      3 

„          ,,      Uniform         8 

„       Flux       263 

„       Force  3,11,12 

„  „      Line  Integral  of ...         ...         ...         ...         ...         ...     265 

„       Hysteresis   ...         ...         ...         ...         ...         ...         ...  93 

,,       Induction  ...         ...         ...         ...         ...         ...         ...       12 

„  „          Calculation  of,  from  Ballistic  Tests 66 

„       Lines  of...         ...         ...         ...         ...         ...         ...         ...         5 

„       Permeability  14,  15,  16,  17 

„       Poles 2 

„       Resistance 268 

„        of  Joints       285,291 

„  5,  „         Effects  of  Compression  on  ...         ...          289 

„       Saturation 52,  155 

„       Susceptibility         18 


390  INDEX. 

PAGE 

Magnetic  Traction 255 

„       Viscosity 127 

Magnetisation,  Curves  of...         ...         ...         ... 52 

Cyclic,  Process  of      75 

„  Effects  of  Stress  on         ...         ...         197 

„  „        Temperature  on 166 

„  Energy  dissipated  in       ...         ....        ...         ...          79,326 

„  Examples  of  Calculation  of •      49,70 

Intensity  of         ., ' 7,8 

„  Lines  of  ...         ...         ...         ...  9 

„  of  a  Long  Rod      30 

„  of  an  Ellipsoid ...  23 

„  Time  Lag  in         128 

Uniform          8,23,27 

Magnetising  Process,  Three  Stages  of 300,309 

Magnetism,  Free         2,26 

„          Residual        <         32,52 

Magnetite  (Dubois),  Experiments  with        ...         ...         ...         ...  162 

Magnetometer,  Mirror      ...         ...         ...         : 41 

Magnetometric  Method 35,37,49 

„  „         Example  of 49 

Magnetomotive  Force ...         ...         ...         ....  265 

Magneto-Optic  Rotation  (Kerr)  ....         ...         ...         ...         ...         ...     158 

Manganese  Steel,  Hadfield's 85 

Matteucci  on  Effects  of  Stress 197,231 

Maxwell:  Line-Integral  of  Magnetic  Force  ...         ...         ...  265 

„        Modification  of  Weber's  Molecular  Theory 298 

„         on  Tension  along  Lines  of  Force  ...         ...         ...  259 

Mayer  (A.)  on  Strains  caused  by  Magnetisation  ...         ...         ...     249 

Mechanical  Hardness,  Influence  of,  on  the  Magnetic  Qualities  of  Iron       80 
Methods  in  Magnetic  Measurements,  Classification  of...         ._,         ...       36 

Mirror  Magnetometer  ...         ...         ...         ...         ...         ...  41 

Model  Illustrating  the  Molecular  Theory ...     349 

Molecular  Accommodation     ...         ...         ...         ...         ...         ...  135 

„         Agitation,  Reduction  of  Hysteresis  by         ...          ...         ...     330 

Molecular  Configuration,  Hysteresis  in        ...  34S 

„         Groups,  Study  of         ...         ...         ...  ..         301 

„         Magnets  Constrained  by  their  Mutual  Forces  ...         ...  299 

„        Theory,  Contributions  to 299 

„  „         Experimental  Study  of  ...         349 

„  „         in  Relation  to  the  Effects  of  Temperature  ....     334 

„  „  „  Vibration  ...  330 

.  Hysteresis 326 

„  „        Poisson's 294 

Weber's          136,294,297 

Moment  of  a  Magnet ...         ...         ....         ...  3 

Mordey  (W.  M.):  Experiments  on  Transformers         ...         193 

Morris  (D.  K.) :  Researches  on  Effects  of  Temperature   ...        ...          ISO 


INDEX.  391 

PAGE 

Nagaoka  on  Effects  of  Twist        ,         ...     240 

Newall  (H.  F.)  :  Effect  of  Cutting  a  Bar 285 

„  „         Experiment  Showing  Hysteresis  in  Recalescence  ...     184 

Nickel ,  Critical  Temperature  of        176 

.,       Curves  of  Permeability  of          91 

„       Effects  of  Stress  in 192,198 

,,  ,,          Temperature  in  ...         ...         ...         ...         ...     175 

„       Experiments  with      ...          ..  ...         ...         ...         ...    86,  153 

,,       Nagoaka's  Experiments  with     ...         ...         ...         ...         .-     240 

„       Rowland's  „  „  „.  88 

„      Steel          85 

„          „     Double  Condition  of 185 

One-Pole  Method 40 

Optical  Methods  (Dubois)      158 

Osmond :  Experiments  on  Recalescence  .    ...         163,185 

Paramagnetic  Substances      ...         ...         ...          ...         ...         ...  16 

Parshall  (H.  F.) 112 

andHobart 367,379 

Partridge  (G.  W.) 193 

Perfect  Magnetic  Circuit       263 

Permeability  Bridge         ...         ...         ...         ...         ...         ...         ...     356 

,,          Curves  of  Nickel  under  Compression  ...         ....  206 

Differential...         56 

„          Magnetic  13,  16 

„          under  Small  Magnetic  Forces      ...         ...         ...         ...     124 

„      Strong        „  „  136,  152 

Permeameter         ...         260 

Pianoforte  Steel  Wire,  Tests  of         83 

Poisson's  Molecular  Theory 294 

Polarised  State  7 

Pole,  Strength  of  a  3,8 

Poles,  Magnetic  ...         ...         ...         ...         ...         ...         ...  2 

Practical  Magnetic  Testing          ...         ...         ...         ...         ...         ...     355 

Pull,  Effects  of  •     198 

Rayleigh  (Lord)  54 

„  „      Energy  of  Magnetisation         99 

„  „      Experiments  with  Weak  Magnetic  Forces          ....  124 

Recalescence  (Barrett)      ...         ...         ...         ...         ...         ...         ...     167 

„  Osmond's  Experiments  ...         .«         ...         ...  168,  185 

„  Hysteresis  in          184 

Repetition  of  Magnetic  Processes      ...         ...         ...         ...         ...  338 

Residual  Effects  of  Stress  230 

Mu-gnetism   ...         ....         ...         ...         ...         ...         ...      32,  52 

„        Experiments  on     ...         ...         ...         ...         ...     316 

„        Graphic  Process  of  Determining       ...         ...  278 

„        in  Iron         74 

„        Proportion  cf  to  Induced       ...         ...         ...318,322 

„         Reduced  by  Vibration      112 


392  INDEX. 

PAGE 

Resistance,  Magnetic ...         ...         ...         268 

„  „        of  Joints     ..         ...         ...         ...         285 

Retentiveness" «         32,  314 

„  and  Residual  Magnetism  explained  by  reference  to 

the  Molecular  Theory          314,323 

Reversals,  Method  of  Demagnetising  by      ...         ...         ...         ...  46 

Rheostat,  Liquid   ...         ...         ...         ...         ...         ...         ...         ...       44 

Ring  Magnet 8,13,271 

„          „      with  an  Air  Gap      275 

Rings,  Forms  of  ...         ...         ...         67 

„      Magnetic  Forces  in  ...         ...         ...         ...         66 

„     Tests  of  by  the  Ballistic  Method      64 

Roberts- Austen  (Sir  W.)  191 

Roget(S.  R.)  :  Researches  on  the  "Ageing"  of  Iron        193 

Rowland's  Curves  of  Permeability  and  Susceptibility  ...         ...       88 

Experiments         52,59,60,63,73,88,90 

„  „  on  Effects  on  Temperature    ...         ...         ...     169 

Saturation,  Magnetic 52,156 

„  „        in  Relation  to  Molecular  Theory  ...         ...     294 

Self -Demagnetising  Force      14,33 

„  „  „      Graphic  Process  of  allowing  for     ...         ...       54 

Solenoid,  Field  due  to  a          ...         ...         ...         ...          ...         ...  6 

S  pecific  Magnetic  Re  sistance       268 

Speed,  Influence  of,  on  Magnetic  Hysteresis  108 

Sphere,  Uniformly  Magnetised    ...         ...         ...         ...       27 

Split-Ring  Magnet      275 

Stages  of  the  Magnetising  Process         ...         ...         ...         ...         ...     300 

Steel,  Curves  of  Magnetisation  of      84,109,174 

„      Magnetic  Qualities  of        ...         ...       82 

„      Permanent  Magnetic  Set  in ...         ...         ...  344 

Steels,  Non-Magnetic        85 

„       Various,  under  Strong  Magnetic  Forces     ....         ...         ...  152 

Steinmetz  (C.  P.) «         ...        111,381 

Stoletow's  Curve  of  Magnetisation  ...         83 

„          Experiments  on  Susceptibility        ...         ...         ...  52,59 

Strain  caused  by  Magnetisation        ...         ...         ...  249 

„      (Elastic),  Effects  of,  in  relation  to  the  Molecular  Theory       ...     344 

„       (Permanent),  Effects  of          336 

Strength  of  a  Pole  3,8 

Stress,  Effects  of         197,344 

„      Internal,  due  to  Magnetisation  ...         254 

Strong  Fields,  Effects  of        136 

Susceptibility,  Differential  ...         ...         ...         ...         56 

„  Magnetic        ...         ...         ...         ...  18 

„  „        Increase  of ,  by  Vibration     112 

Swedish  Wrought  Iron  under  Strong  Magnetic  Forces     ....         ...  141 

Swinburne  (J.)       327 

Tanakadate  :  Experiments  with  Rods  of  Various  Lengths          ,„,  79 


INDEX.  393 

PACK 

Tanakadate  :  Experiments  on  Heating  due  to  Hysteresis      Ill 

Tait :  Change  of  Thermoelectric  Quality  of  Iron  at  Critical  Tempera- 
ture    167 

Temper,  Effects  of,  in  Steel         83 

Temperature,  Effect5?  of,  in  the  Magnetising  Process         .».          ...   166,  333 

Tension  along  Lines  of  Force       ...         259 

„       Effects  of 197 

Thermoelectric  Quality,  Hysteresis  in   ...         ...         ...         ...         ...     230 

Thompson  (S.  P.)  on  Tractive  Force  ... 257 

„  „         Permeameter  ...         .«         ...         ...         ...     260 

Thomson  (J.  J.)  :  Effect  of  Cutting  a  Bar  .„         285 

„         on  the  Effects  of  Stress         -.         ...     224 

Time  Lag  in  the  Magnetisation  of  Iron        ...         ...         ...         ...     56,  335 

„  „  „         Experiments  on         ...         ...     128 

Tomlinson  (H.)  on  Molecular  Accommodation        ....         ....         ..„  135 

„  „        on  Effects  of  Stress  in  Nickel  202 

Torsion,  Effects  of       ,         231 

Tractive  Force  in  Divided  Magnets        «         ....     255 

„  „     Measurement  of  Magnetisation  by  Means  of         ....  259 

Transformers,  Heating  of  the  Cores  in ...         ...     103 

Transient  Currents  produced  by  Twist        ...         ...         ...         ...  237 

Trouton  (F.  T.) :  Experiment  showing  Hysteresis  in  Recalescence  ...     184 

Tubes  of  Magnetic  Induction  263 

Tungsten  Steel       83 

Uniform  Magnetic  Field         ...          ...          ...          ...          ...          ...  6 

„         Magnetisation     ...          ...          ...          ...          ...          .„         8,  23,  27 

Unit  Quantity  of  Magnetism  ...          ...          ...          ...          ....  3 

Vibration,  Effects  of          111,330 

Vickers'  Tool  Steel  under  Strong  Magnetic  Forces  151 

Villari :  Reversal  of  Effects  of  Stress -.197,224,  236 

Viscosity,  Magnetic     ...         ...         ...         ...         ....         .«         .~  127 

Waltenhofen,  Von  :  Experiments  of      74,340 

Warburg  (E.) :  Dissipation  of  Energy  in  Magnetisation    ...         ...    99,  111 

Weak  Fields,  Effects  of 124 

Weber's  Theory  of  Diamagnetism    ...         ....         ...         ...         ...  353 

„  „         Molecular  Magnets 136,294 

Wertheim  on  Effects  of  Torsion       231 

Wiedemann  on  Effects  of  Stress  198 

„  „  Torsion 231 

„  Hypothesis  of  Molecular  Friction        .«         ....         ...     298 

„  Torsional  Strain  produced  by  Superposed  Magnetisms   236 

Wilson  (E.)  123 

Yoke  for  the  Ballistic  Tests  of  Bars 68,  361 

„     with  Two  Bars         70,362 

Zehnder  on  Effects  of  Twist  ...  240 


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Aitken—  HANDBOOK   OF  COMMERCIAL  TELEPHONY.     By 

W.  Aitken.    In  the  press. 

Anderson—  BOILER  FEED  WATER  :  Its  Impurities,  Analysis  and 

Purification.     By  Fred.  A.  Anderson,  B.Sc.  (Lond.),  F.I.C.,  F.C.S. 

Ayrton—  THE    ELECTRIC    ARC.      By   Mrs.   Ayrton,    M.I.E.E. 

Very  fully  Illustrated.    Price  123.  6d. 

Abstract  from  Authors  Preface.  —  This  book  owes  its  origin  to  a  series  of  articles 
published  in  The  Electrician  in  1895-6.  In  experimenting  on  the  arc  my  aim  was  not  so  much  to  add 
to  the  large  number  of  isolated  facts  that  had  already  been  discovered,  as  to  form  some  idea  of  the 
bearing  of  these  upon  one  another,  and  thus  to  arrive  at  a  clear  conception  of  what  takes  place  in 
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and  opened  up  fresh  questions,  to  be  answered  in  their  turn  by  new  experiments.  Thus  the  subject 
grew  and  developed  into  what  may  almost  be  termed  a  natural  way.  The  experiments  of  other 
observers  have  been  employed  in  two  ways  :  (i)  In  confirmation  of  theory  developed  from  my  own 
experiments,  and  (a)  as  the  basis  of  theory  for  which  further  tests  ware  devised.  M.  BlondeFs 
interesting  and  systematic  researches,  the  admirable  work  of  Mr.  A.  P.  Trotter,  and  Prof. 
Ayrton's  Chicago  Paper  were  all  laid  under  contribution,  and  the  deductions  drawn  1rom  them 
tested  by  new  experiments.  The  excellent  work  done  by  men  whose  names  are  quite  unfamiliar  to 
us  in  England,  including  Nebel,  Feussner,  Luggin,  Granquist  and  Herzfeld,  has  been  utilised. 

Raines—  BEGINNER'S    MANUAL    OF    SUBMARINE    CABLE 

TESTING  AND  WORKING,  By  G.  M.  Baines.  Second  Edition.  Cloth  Bound. 
73.  6d.  nett,  post  free  8s. 

This  book  has  been  written  to  meet  the  requirements  of  those  about  to  commence  the  study 
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obtained  of  them.  With  regard  to  the  algebraical  portion  of  the  study,  all  the  formulae  have  been 
worked  out  step  by  step,  and,  where  convenient,  have  been  supplemented  by  arithmetical 
equivalents.  The  book  is  divided  into  18  chapters,  and  deals  with  :  Batteries,  Ohm's  Law,  Joint 
Resistance,  Wheatstone  Bridge,  Bridge  Measurements,  Insulation  Test  by  Direct  Deflection, 
Inductive  Capacity,  Internal  Resistance  and  E.M.F.  of  a  Battery,  &c.,  Current  Strength  in 
Wheatstone  Bridge,  &c.,  Tests  of  Broken  or  Faulty  Cables,  and  Description  of  Apparatus.  &c. 

Beaumont—  THE   STEAM-ENGINE   INDICATOR  AND  INDI- 

CATOR DIAGRAMS.    Edited  by  W.  W.  Beaumont,  M.I.C.E.,  M.I.M.E.,  &c.    New 

and  Enlarged  Edition,  Now  Ready.    6s.  nett,  post  free. 

The  object  of  this  book  is  to  place  in  the  hands  of  students  and  practical  men  a  concise 
guide  to  the  objects,  construction  and  use  of  the  indicator,  and  to  the  interpretation  of  indicator 
diagrams.  Lengthy  discussion  of  theoretical  or  hypothetical  matters  has  been  avoided.  The 
behaviour  of  steam  and  its  expansion  under  different  conditions  have  been  treated  in  a  simple 
manner  so  far  as  these  questions  are  important  to  the  consideration  of  indicator  diagrams  in 
their  most  usual  practical  applications. 

Bond—  RATING    OF    ELECTRIC     LIGHTING,     ELECTRIC 

TRAMWAY  AND  SIMILAR  UNDERTAKINGS.    By  W.   G.  Bond.    Cloth,  8vo, 

price  2s.  6d.  net. 

This  little  book  is  intended  for  the  use  of  Directors,  Secretaries,  Engineers  and  other 
Officials  connected  with  Electric  Traction,  Lighting  and  Power  Distribution  Companies.  Th<=> 
chief  object  of  the  Author  has  been  to  enable  those  who  are  not  familiar  with  the  principles  and 
practice  of  rating  to  ascertain  for  themselves  whether  the  Rateable  Value  of  their  property  is 
reasonable  or  excessive,  and  thus  avoid  unnecessary  expense  at  the  outset. 

Boult—  COMPREHENSIVE  INTERNATIONAL  WIRE  TABLES 

FOR  ELECTRIC  CONDUCTORS.     By  W.  S.  Boult.    Price  43.  post  free. 

Broughton—  ELECTRIC  CRANES  AND  HOISTS.     By  H.  H. 

Broughton.     In  Ihe  Press. 

Carter—  MOTIVE  POWER  AND  GEARING  FOR  ELECTRICAL 

MACHINERY:  A  Treatise  on  the  Theory  and  Practice  of  the  Mechanical  Equipme.it 
of  Power  Stations  for  Electric  Supply,  and  for  Electric  Traction.  By  the  late  E.  Tremlett 
Carter,  C.E.,  M.I.E.E.  650  pages,  200  Illustrations,  Scale  Drawings  and  Folding 
Plates,  and  over  80  Tables  of  Engineering  Data.  In  one  volume.  New  edition  r°vised 
by  G.  THOMAS-DA  VIES.  Now  Ready.  Price  ias.  6d.  nett,  post  free  135. 

Part     I.—  Introductory.  Part  II.—  The  Steam  Engine.  Part  III.—  Gas  and  Oil  Engines. 

Part  IV.—  Water  Power  Plant.  Part  V  —  Gearing.  Part  VI.—  Types  of  Power  Stations. 


engneerng 


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ering  students  the  latest  and  most  approved  practice  in  the  equipment  and  working  of 


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4     ) 


mechanical  plant  in  electric  power  generating  stations.  Every  part  of  the  work  has  been  brought 
completely  up  to  date  ;  and  especially  in  the  matter  of  the  costs  of  equipment  and  working  the 
latest  available  information  has  been  given.  The  treatise  deals  with  Steam  Gas,  Oil  and 


ht 
e 

given.  The  treatise  deals  with  Steam,  Gas,  Oil  and 
H}-draulic  Plant  and  Gearing;  and  it  deals  with  these  severally  from  the  three  standpoints  of 
(ij  Theory,  (2)  Practice  and  (3)  Costs. 

"MOTIVE  POWER  AND  GEARING  FOR  ELECTRICAL  MACHINERY"  is  a  handbook  of  modern 
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engineer  throughout  the  world,  as  it  constitutes  the  only  existing  treatise  on  the  Economics  of 
Motive  Power  and  Gearing  for  Electrical  Machinery. 

Cooper—  PRIMARY   BATTERIES:   THEIR   CONSTRUCTION 

AND  USE.    By  W.  R.  Cooper,  M.A.    Fully  Illustrated.     Price  IDS.  6d.  nett. 

Authors  Preface  —  Extract,  —  Primary  Batteries  form  a  subject  from  which  much  has  been 
hoped,  and  but  little  realised.  But  even  so,  it  cannot  be  said  that  the  advance  has  been  small  ; 
and  consequently  no  apology  is  offered  for  the  present  volume,  in  which  the  somewhat  scattered 
literature  of  the  subject  has  been  brought  together.  Recent  years  have  seen  important  additions 
to  the  theory  of  the  voltaic  cell,  and  therefore  a  considerable  number  of  pages  have  been  devoted 
to  this  part  of  the  subject,  although  it  is  impossible  to  do  more  than  give  a  superficial  sketch  of 
the  theory  in  a  volume  like  the  present.  With  regard  to  the  practical  part  of  the  subject,  this 
volume  is  not  intended  to  be  encyclopaedic  in  character  ;  the  object  has  been  rather  to  describe 
those  batteries  which  are  in  general  use,  or  of  particular  theoretical  interest.  As  far  as  possible, 
the  Author  has  drawn  on  his  personal  experience,  in  giving  practical  results,  which,  it  is  hoped, 
will  add  to  the  usefulness  of  the  book.  Owing  to  the  importance  of  the  subject,  Standard  Cells 
have  been  dealt  with  at  some  length.  Those  cells,  however,  which  are  no  longer  in  general  use 
are  not  described  ;  but  recent  work  is  summarised  in  some  detail  so  as  to  give  a  fair  idea  of  our 
knowledge  up  to  the  present  time.  It  has  also  been  thought  well  to  devote  a  chapter  to  Carbon- 
Consuming  Cells.  Very  little  has  been  written  upon  this  subject,  but  it  is  of  great  interest,  and 
possibly  of  great  importance  in  the  future. 

Cooper—  See  "THE  ELECTRICIAN"  PRIMERS,  page   n. 
Dick  and  Fernie—  MAINS  AND  CABLES.     By  J.  R.  Dick,  B.Sc., 

and  F.  Fernie. 

Down—  "  THE  ELECTRICIAN"  HANDY  COPPER  WIRE 

TABLES  AND  FORMULAE  FOR  EVERYDAY  USE  IN  FACTORIES  AND 
WORKSHOPS.  By  P.  B.  Down,  Wh.Ex.,  A.M.I.M.E.  Price  2s.  6d.  nett. 

Ewing—  MAGNETIC    INDUCTION   IN   IRON   AND   OTHER 

METALS.  By  Prof.  J.  A.  Ewing,  M.A.,  B.Sc.,  F.R.S.,  Professor  of  Mechanism  and 
Applied  Mechanics  in  the  University  of  Cambridge.  382  pages,  173  Illustrations.  Price 
los.  6d.  nett.  Third  Edition,  Second  Issue. 

Synopsis  of  Contents.  —  After  an  introductory  chapter,  which  attempts  to  explain  the 
fundamental  ideas  and  the  terminology,  an  account  is  given  of  the  methods  which  are  usually 
employed  to  measure  the  magnetic  quality  of  metals.  Examples  are  then  quoted,  showing  the 
results  of  such  measurements  for  various  specimens  of  iron,  steel,  nickel  and  cobalt.  A  chapter 
on  Magnetic  Hysteresis  follows,  and  then  the  distinctive  features  of  induction  by  very  weak  and 
by  very  strong  magnetic  forces  are  separately  described,  with  further  description  of  experimental 
methods,  and  with  additional  numerical  results.  The  influences  of  Temperature  and  ot  Stress  are 
discussed.  The  conception  of  the  Magnetic  Circuit  is  then  explained,  and  some  account  is  given  ot 
experiments  which  are  best  elucidated  by  making  use  of  this  essentially  modern  method  of  treatment. 

Fisher—  THE  POTENTIOMETER  AND  ITS   ADJUNCTS.     (A 

Universal  System  of  Electrical  Measurement.)  By  W.  Clark  Fisher.  New  Edition  in 
Preparation, 

The  extended  use  of  the  Potentiometer  System  of  Electrical  Measurement  will,  it  is  hoped, 
be  sufficient  excuse  for  the  publication  of  this  work,  which,  while  dealing  with  the  main  instru- 
nient,  its  construction,  use  and  capabilities,  would  necessarily  be  incomplete  without  similar 
treatment  of  the  various  apparatus  which  extend  the  range  and  usefulness  of  the  whole  system. 

The  engineer  or  practical  man  demands  that  he  shall  be  shown  results  quickly,  plainly  and 
accurately  with  a  minimum  of  trouble,  understanding,  and  consequently  "  Time,"  and  on  that 
account  prefers  —  like  all  good  mechanics  —  to  have  one  good  instrument,  which,  once  understood 
and  easily  manipulated,  can  be  used  in  a  variety  of  ways  to  suit  his  needs.  It  is  to  this  tact, 
undoubtedly,  that  the  "  Potentiometer  "  method  of  measurement  owes  its  popularity.  Its  accuracy 
is  rarely,  if  ever,  impugned.  Measurements  made  by  it  are  universally  accepted  amongst  engi- 
neers, and  it  might  be  well  termed  a  "  universal  "  instrument  in  "  universal  "  use. 

Fleming—  THE  CENTENARY  OF  THE  ELECTRIC  CURRENT. 

jygg  —  1899.    By  Prof.  J.  A.  Fleming,  F.R.S.     With  Illustrations  of  early  apparatus  and 

interesting  Chronological  Notes.    In  neat  paper  covers  is.  nett,  post  free  is.  3d.     Bound 

_  cloth  as.  nett,  post  free.  _  _______  _ 

"  THE  ELECTRICIAN  "  PRINTING  &  PUBLISHING  CO.,  LTD., 
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(     5     ) 

Fleming— A  HANDBOOK  FOR  THE  ELECTRICAL  LABORA- 
TORY AND  TESTING  ROOM  By  Dr.  J.A.Fleming,  M.A.,  F.R.S.,  M.R.I.,  &c. 
Vol.  I.,  price  125.  6d.  nett,  post  free  133.  Vol.  II.,  145.  nett. 

This  Handbook  has  been  written  especially  to  meet  the  requirements  of  Electrical 
Engineers  in  Supply  Stations,  Electrical  Factories  and  Testing  Rooms.  The  Book  consists  of  a 
series  ot  Chapters  each  describing  the  most  approved  and  practical  methods  of  conducting  some 
one  class  of  Electrical  Measurements,  such  as  those  of  Resistance,  Electromotive  Force,  Current, 
Power,  &c.,  &c.  It  does  not  contain  merely  an  indiscriminate  collection  ot  Physical  Laboratory, 
processes  without  regard  to  suitability  for  Engineering  Work.  The  Author  has  brought  to 
its  compilation  a  long  practical  experience  of  the  methods  described,  and  it  will  be  found  to  be  a 
digest  of  the  best  experience  in  Electrical  Testing.  The  Volumes  contain  a  Chapter  on  the 
Equipment  of  Electrical  Laboratories  and  numerous  Tables  of  Electrical  Data,  which  will  render 
it  an  essential  addition  to  the  library  of  every  practical  Electrical  Engineer,  Teacher  or  Student. 

SYNOPSIS  OF  CONTENTS. 


Vol.  I. 

Chapter  I.— Equipment  of  an  Electrical  Test- 
ing Room. 
„      II.— The    Measurement    of    Electrical 

Resistance. 
„    III. — The     Measurement     of     Electric 

Current. 
„     IV.— The  Measurement  of  E.M.F. 

V. — TheMeasurementofElectricPower. 


Vol.  II. 

Chapter  I. — The  Measurement  of  Electric 
Quantity  and  Energy. 

„  II. — The  Measurement  of  Capacity 
and  Inductance. 

„     III.— Photometry. 

„      IV. — Magnetic  and  Iron  Testing. 

„  V. — Dynamo,  Motor  and  Transformer 
Testing. 


Fleming— THE    ALTERNATE     CURRENT    TRANSFORMER 

IN  THEORY  AND  PRACTICE.    By  Prof.  J.  A.  Fleming,  M.  A.,  D.Sc.,  F.R.S.,  M.R.I., 
&c.    Vol.  I.     New  Edition — Almost  entirely  Rewritten,   and  brought  up  to  date.     More 
than  600  pages  and  213  illustrations,  i2s.  6d.  post  free;  abroad,  135.  Vol.  II.    Third  issue. 
More  than  600  pages  and  over  300  illustrations,  123.  6d.  post  free  ;  abroad  133. 
Since  the  first  edition  of  this  Treatise  was  published,  the  study  of  the  properties  and  appli- 
cations of  alternating  electric  currents  has  made  enormous  progress The  Author  has, 

accordingly,  rewritten  the  greater  part  of  the  chapters,  and  availed  himself  of  various  criticisms, 
with  the  desire  of  removing  mistakes  and  remedying  defects  of  treatment.  In  the  hope  that  this 
will  be  found  to  render  the  book  still  useful  to  the  increasing  numbers  of  those  who  are  practically 
engaged  in  alternating-current  work,  he  has  sought,  as  far  as  possible,  to  avoid  academic  methods 
and  keep  in  touch  with  the  necessities  of  the  student  who  has  to  deal  with  the  subject  not  as  a 
basis  for  mathematical  gymnastics  but  with  the  object  of  acquiring  practically  useful  knowledge. 

Dr.  Fleming's  manual  on  the  Alternate-Current  Transformer  in  Theory  and  Practice  is 
recognised  as  the  text  book  on  the  subject.  Vol.  I.,  which  deals  with  '•'  The  Induction  of  Electric 
Currents,"  has  passed  through  three  editions,  each  edition  having,  in  its  turn,  passed  through 
several  issues.  Vol.  II.,  which  treats  of  ''The  Utilisation  of  Induced  Currents,"  has  also  passed 
through  numerous  issues. 

Fleming— ELECTRICAL  LABORATORY  NOTES  AND  FORMS. 

Arranged  and  prepared  by  Dr.  J.  A.  Fleming,  M.A.,  F.R.S.,  &c. 

This  important  Series  of  Notes  and  Forms  for  the  use  of  Students  in  University  and  other 
Electro-technical  Classes  has  a  world-wide  reputation,  and  many  thousands  of  copies  have  been 
sold.  From  time  to  time,  as  considered  desirable,  the  Notes  and  Forms  have  been  corrected  or 
re-written,  but  the  original  divisions  of  the  forty  Forms  into  "Elementary"  and  "Advanced" 
has  hitherto  been  observed.  The  object  of  this  arbitrary  division  has  now  been  fully  served,  and 
it  has  been  decided  that  in  future  only  the  numerical  order  shall  be  retained.  At  the  same  time 
itis  realised  that  the  timehas  come  for  additions  to  be  made  to  the  original  Set,  and  Dr.  Fleming 
lias  written  Ten  Additional  Notes  and  Forms  (Nos.  41  to  50).  It  should  be  remembered  that  the 
numerical  order  observed  in  the  above  list  has  no  relation  to  the  difficulty  or  class  sequence  of  the 
exercise,  but  is  simply  a  reference  number  for  convenience.  The  Subjects  of  the  additional  Notes 
and  Forms  are : — 


No.  SUBJECT. 

41.  Determination  of  Dynamo  Efficiency  by 

Routin's  Method. 

42.  Separation  ot  Hysteresis  and  Eddy  Cur- 
rent   Losses    in     Continuous-Current 
Dynamo  Armatures. 

43.  Efficiency  Test  of  Two   Equal  Trans- 

formers by  the  Differential  (Sumpner*s) 
Method. 

44.  Measurement    of    the    Efficiency    and 
Power  Factor  of  a  Polyphase  Induc- 
tion Motor  by  the  Wattmeter  Method. 


No.  SUBJECT. 

45.  Determination   of   the  Characteristic 
Curves  of  Dynamo  Machines. 

46.  The  Absolute  Measurement  of  Capa- 

city. 

47.  The  Measurement  of  Inductances. 

48.  The  Test  of  a  Rotary  Converter. 

49.  The  Parallelisation  of  Alternators. 

50.  The  Examination  of  an  Alternating- 

Current  Motor. 


These  "  Electrical  Laboratory  Notes  and  Forms  "  have  been  prepared  to  assist  Teachers, 
Demonstrators  and  Students  in  Electrical  Laboratories,  and  to  enable  the  Teacher  to  economise 
time.  They  now  consist  of  a  series  of  50  Exercises  in  Practical  Electrical  Measurements  and 
Testing.  For  each  of  these  Exercises  a  four-page  Report  Sheet  has  been  prepared,  two  and  some- 
times more  pages  of  which  are  occupied  with  a  condensed  account  of  the  theory  and  practical  in- 
structions for  performing  the  particular  Experiment,  the  other  pages  being  ruled  up  in  lettered 
columns,  to  be  filled  in  by  the  Student  with  the  observed  and  calculated  quantities.  Where  simple 
diagrams  will  assist  the  Student,  these  have  been  supplied.  These  Exercises  are  perfectly  general, 
and  can  be  put  into  practice  in  any  Laboratory. 

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Fleming— HERTZIAN    WAVE     WIRELESS     TELEGRAPHY ; 

A  Reprint  of  a  series  of  articles  in  the  "  Popular  Science  Monthly,"  based  upon  Dry 
Fleming's  Cantor  Lectures  before  the  Society  of  Arts,  1903.  By  Dr.  J.  A.  Fleming, 
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Fleming.— ELECTRIC  LAMPS  AND  ELECTRIC  LIGHTING. 

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trated, handsomely  bound,  on  good  paper,  price  6s.  nett 

The  original  aim  of  a  course  of  four  lectures  by  Prof.  J.  A.  Fleming  on  "  Electric  Illumina- 
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and  problems  concerned  in  the  modern  applications  of  electricity  for  illumination  purposes  as 
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Fleming— THE  ELECTRONIC  THEORY  OF  ELECTRICITY. 

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Fynn— THE  CLASSIFICATION  OF  ALTERNATE  CURRENT 

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Geipel   and    Kilgour— A   POCKET-BOOK    OF    ELECTRICAL 

ENGINEERING  FORMULAE,  &c.  By  \V.  Geipel  and  H.  Kilgour.  Second  Edition. 
800  pages.  75.  6d.  nett ;  post  free  at  home  or  abroad,  js.  gd. 

With  the  extension  of  all  branches  of  Electrical  Engineering  (and  particularly  the  heavier 
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articles  and  hints  on  the  construction  and  management  of  various  plant  and  machinery. 

Gerhardi— ELECTRICITY  METERS,  THEIR  CONSTRUCTION 

AND    MANAGEMENT.     A  Practical  Manual  for  Central  Station  Engineers,  Distri- 
buting Engineers,  and  Students.    By  C.  H.  W.  Gerhardi.    8vo.   Fully  illustrated.  95.  nett. 
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a  volume  in  "  THE  ELECTRICIAN  "  Series,  will  bo,  published  shortly.     The  Author  has  had  many 
years'  exceptional  experience  with  Electricity  Meters  as  chief  ot  the  Testing  Department  of  the 
largest  electricity  supply  undertaking  in  the  United  Kingdom.     Mr.  Gerhardi's  intimate  acquain- 
tance with  the  working  of  all  existing  meters  on  the  market,  and  with  the  details  of  their  construc- 
tion, is  a  guarantee  that  the  book  will  meet  the  requirements  of  those  engaged  in  work  in  which  the 
Electricity  Meter  forms  an  essential  part.     In  the  division  of  the  book  devoted  to  "  Testing,"  Mr. 
Gerhardi's  experience  will  prove  of  the  greatest  service  to  supply  station  engineers  and  managers. 

Goldschmidt— ALTERNATING  CURRENT  MOTORS.     By  Dr. 

R.  Goldschmidt.     In  the  Press. 

Gore— THE    ART    OF    ELECTROLYTIC    SEPARATION    OF 

METALS   (Theoretical   and  Practical).      By  George  Gore,  LL.D.,  F.R.S.     Over  300 

pages,  106  illustrations.    Price  xos.  6d.  post  free. 

Dr.  Gore's  work  is  ot  the  utmost  service  in  connection  with  all  classes  of  electrolytic  work  con- 
nected with  the  refining  of  metals.  The  book  contains  both  the  science  and  the  art  of  the  subject 
(both  the  theoretical  principles  upon  which  the  art  is  based  and  the  practical  rules  and  details  of  tech- 
nical application  on  a  commercial  scale),  so  that  it  is  suitable  for  both  students  and  manufacturers. 

Gore — ELECTRO-CHEMISTRY.  By  Dr.  G.  Gore.  Price  25.  post  free. 

At  the  time  when  this  book  first  appeared  no  separate  treatise  on  Electro-Cheraistry 
existed  in  the  English  language,  and  Dr.  Gore,  whose  books  on  electro-metallurgy,  electro- 
deposition  and  other  important  branches  of  electro-technical  work  are  known  throughout  the 
world,  has  collected  together  a  mass  of  useful  information  and  has  arranged  this  inconsecutive 
order,  giving  brief  descriptions  of  the  known  laws  and  general  principles  which  underlie  the 
Subject  of  Electro-Chemistry.  A  very  copious  index  is  provided. 

Hawkins— THE   THEORY   OF   COMMUTATION.      By   C.   C. 

Hawkins,  M.A.,  M.I.E.E.     Paper  covers,     as.  6d.  nett. 

Heaviside—  "  ELECTRICAL  PAPERS."     In  Two  Volumes.    By 

Oliver  Heaviside.     Price  £3  :  33.  nett. 

The  first  twelve  articles  of  Vol.  1.  deal  mainly  with  Telegraphy,  and  the  next  eight  with  the 
Theory  of  the  Propagation  of  Variations  of  Current  along  Wires.  Then  follows  a  series  of 
Papers  relating  to  Electrical  Theory  in  general. 

The  contents  of  Vol.  II.  include  numerous  Papers  on  Electro-Magnetic  Induction  and  its 
Propagation,  on  the  Self-induction  of  Wires,  on  Resistance  and  Conductance  Operators  and 
their  Derivatives  Inductance  and  Permittance,  on  Electro-Magnetic  Waves,  a  general  solution 
of  Maxwell's  Electro-Magnetic  Equations  in  a  Homogeneous  Isotropic  Medium,  Notes  on  Nomen- 
clature, on  the  Theory  of  the  Telephone,  on  Hysteresis,  Lightning  Conductors,  &c. 

These  two  Volumes  are  srarce  and  are  not  likely  to  be  reprinted. 

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(     7     ) 
Heaviside—  ELECTROMAGNETIC  THEORY.    By  Oliver  Heavi- 

side.    Vol.1.   Second  issue.    466  pages.   Price  I2s.  6d.,  post  free  133.    Vol.11.   568  pages. 
Price  I2s.  6d.  post  free  ;  abroad,  135. 

Extract  from  Preface  to  Vol.  I.  —  This  work  is  something  approaching  a  connected  treatise 
on  electrical  theory,  though  without  the  strict  formality  usually  associated  with  a  treatise.  The 
following  are  some  of  the  leading  points  in  this  volume.  The  first  chapter  is  introductory.  The 
second  consists  of  an  outline  scheme  of  the  fundamentals  of  electromagnetic  theory  from  the 
Faraday-Maxwell  point  of  view,  with  some  small  modifications  and  extensions  upon  Maxwell's 
equations.  The  third  chapter  is  devoted  to  vector  algebra  and  analysis,  in  the  form  used  by  me 
in  former  papers.  The  fourth  chapter  is  devoted  to  the  theory  of  plane  electromagnetic  waves, 
and,  being  mainly  descriptive,  may  perhaps  be  read  with  profit  by  many  who  are  unable  to  tackle 
the  mathematical  theory  comprehensively.  I  have  included  in  the  present  volume  the  application 
of  the  theory  (in  duplex  form)  to  straight  wires,  and  also  an  account  of  the  effects  of  self- 
induction  and  leakage,  which  are  of  some  significance  in  present  practice  as  well  as  in  possible 
future  developments. 

Extract  from  Preface  to  Vol.  II.  —  From  one  point  of  view  this  volume  consists  essentially 
of  a  detailed  development  of  the  mathematical  theory  of  the  propagation  of  plane  electro- 
magnetic waves  in  conducting  dielectrics,  according  to  Maxwell's  theory,  somewhat  extended 
From  another  point  of  view,  it  is  the  development  of  the  theory  of  the  propagation  of  waves  along 
wires.  But  on  account  of  the  important  applications,  ranging  from  Atlantic  telegraphy,  through 
ordinary  telegraphy  and  telephony,  to  Hertzian  waves  along  wires,  the  Author  has  usually 
preferred  to  express  results  in  terms  of  the  concrete  voltage  and  current,  rather  than  the  specific 
electric  and  magnetic  forces  belonging  to  a  single  tube  of  flux  of  energy.  .  .  .  The  theory  of 
the  latest  kind  of  so-called  wireless  telegraphy  (Lodge,  Marconi,  &c.)  has  been  somewhat 
anticipated,  since  the  waves  sent  up  the  vertical  wire  are  hemispherical,  with  their  equatorial 
bases  on  the  ground  or  sea,  wliich  they  run  along  in  expanding.  (See  \  60,  Vol.  I.  ;  also  $393  in 
this  volume.)  The  author's  old  predictions  relating  to  skin  conduction,  and  to  the  possibilities  of 
long-distance  telephony  have  been  abundantly  verified  in  advancing  practice;  and  his  old 
predictions  relating  to  the  behaviour  of  approximately  distortionless  circuits  have  also  received 
fair  support  in  the  quantitative  observation  of  Hertzian  waves  along  wires. 

Vol.  III.  is  in  preparation,  and  ia  nearly  ready. 


Jehl—  CARBON     MAKING    FOR    ALL    ELECTRICAL    PUR- 

POSES.     By  Francis  Jehl.     Fully  illustrated.     Price  IDS.  6d.  post  free. 

This  work  gives    a    concise    account    of   the  process  of  making    High  Grade  and  other 
Carbon  for  Electric  Lighting,  Electrolytic,  and  all  other  electrical  purposes. 


CONTENTS. 


Chapter    I. — Physical  Properties  of  Carbon. 

,,      II. — Historical  Notes. 

,,      III. — Facts  concerning  Carbon. 

„  IV. — The  Modern  Process  of  Manu- 
facturing Carbons. 

„  V. — Hints  to  Carbon  Manufacturers 
and  Electric  Light  Engineers. 

„      VI.— A  "New  "Raw  Material. 

,,    VII. — Gas  Generators. 

„  VIII.— The  Furnace. 

„  IX.- -The  Estimation  of  High  Tem- 
peratures. 


Chapter    X.— Gas  Analysis. 

,,  XI. — On  the  Capital  necessary  for 
starting  a  Carbon  Works  and 
the  Profits  in  Carbon  Manu- 
facturing. 

.,  XII.— The  Manufacture  of  Electrodes 
on  a  Small  Scale. 

„    XIII.— Building  a  Carbon  Factory. 

„     XIV.— Soot  or  Lamp  Black. 

„       XV.— Soot  Factories. 


Kennelly  and  Wilkinson— PRACTICAL  NOTES  FOR  ELEC- 

TK1CAI.  STUDENTS.     Laws,  Units  and  Simple  Measuring  Instruments.    By  A.  E. 
Kennelly  and  H.  D.Wilkinson.     320  pages,  155  illustrations.     Price  6s.  6d.  post  free. 

These  instructive  Practical  Notes  for  Electrical  Students  were  started  by  Mr.  A.  E. 
Kennelly  prior  to  his  departure  from  England  to  join  the  staff  of  Mr.  Edison  in  the  United 
States,  and  were  continued  and  completed  by  Mr.  H.  D.  Wilkinson,  who  has  prepared  a  work 
which  is  of  great  service  to  students. 

Kershaw- THE  ELECTRIC  FURNACE  IN  IRON  AND  STEEL 

PRODUCTION.  By  John  B.C.  Kershaw,  F.I. C.  Fully  illustrated.  8vo.  Price  33. 6d.  nett. 

Lemstrom— ELECTRICITY  IN  AGRICULTURE  AND  HORTI- 
CULTURE. By  Prof.  S.  Lemstrom.  With  illustrations.  Price  35.  6d.  nett. 

Extract  from  Author  s  Introductory  Remarks. — It  is  well  known  that  the  question  which  is 
the  subject  of  this  book  has  been  a  favourite  field  of  investigation  for  a  century  past.  As  the  sub- 
ject is  connected  with  no  less  than  three  sciences — viz.,  physics,  botany  and  agricultural  physics — 
it  is  in  itself  not  particularly  attractive.  The  causes  which  induced  me  to  begin  the  investigation 
of  this  matter  were  manifold,  and  I  venture  to  hope  that  an  exposition  of  them  will  not  be  with- 
out general  interest. 

Livingstone  — THE  MECHANICAL  DESIGN  AND  CON- 
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Now  Ready.  Price  6s.  nett. 

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(     3     ) 
Lodge- WIRELESS  TELEGRAPHY.— SIGNALLING   ACROSS 

SPACE  WITHOUT  WIRES.  By  Sir  Oliver  J.  Lodge,  D.Sc.,  F.R.S.  New  and 
Enlarged  Edition.  Now  Ready.  Very  fully  illustrated.  Price  55.  nett,  post  free  55.  3d. 
The  new  edition  forms  a  complete  Illustrated  Treatise  on  Hertzian  Wave  Work.  The  Full 
Notes  of  the  interesting  Lecture  delivered  by  the  Author  before  the  Royal  Institution,  London,  in- 
June,  1894,  form  the  first  chapter  of  the  book.  The  second  chapter  is  devoted  to  the  Application1 
of  Hertz  Waves  and  Coherer  Signalling  to  Telegraphy,  while  Chapter  III.  gives  Details  of  other 
Telegraphic  Developments.  In  Chapter  IV.  a  history  of  the  Coherer  Principle  is  given,  including 
Professor  Hughes'  Early  Observations  before  Hertz  or  Branly,  and  the  work  of  M.  Branly. 
Chapters  are  also  devoted  to  "  Communications  with  respect  to  Coherer  Phenomena  on  a  Large 
Scale,"  the  "Photo-Electric  Researches  of  Drs.  Elster  and  Geitel,"  and  the  Photo-Electric 
Researches  of  Prof.  Righi. 

Maurice— ELECTRIC  BLASTING  APPARATUS  AND  EXPLO- 

SIVES,  WITH   SPECIAL  REFERENCE  TO  COLLIERY   PRACTICE.     By  Wm.. 

Maurice,  M.Nat.Assoc.  of  Colliery  Managers,   M.LMin.E.,  A.M.I.E.E.    Now  Ready* 

Price  8s.  6d.nett. 

The  aim  of  this  book  is  to  prove  itself  a  useful  work  of  reference  to  Mine  Managers, 
Engineers  and  others  engaged  in  administrative  occupations  by  affording  concise  information 
concerning  the  most  approved  kinds  of  apparatus,  the  classification  and  properties  of  explosives, 
and  the  best  known  means  of  preventing  accidents  in  the  use  ot  them.  Th»*  work  gives  not  only 
an  explanation  of  the  construction  and  safe  application  of  blasting  appliances,  the  properties  of 
explosives,  and  the  difficulties  and  dangers  incurred  in  daily  work,  but  it  also  serves  as  an  easy 
introduction  to  the  study  ot  electricity— without  at  least  a  rudimentary  knowledge  of  which  no 
mining  official  can  now  be  considered  adequately  trained.  Particular  attention  has  bef*n  devoted 
to  the  problem  of  safe  shot  firing  in  coal  mines,  and  an  attempt  has  been  made  to  present  the 
most  reliable  information  on  the  subject  that  experience  and  recent  research  have  made  possible. 

Maurice— THE  SHOT-FIRERS  HAN  1)1  5OO  K.     In  preparation. 
May— MAY'S  BELTING  TABLE.    Showing  the  Relations  between— 

(i)The  number  of  revolutions  and  diameter  of  pulleys  and  velocitv  of  belts :  (2)  'Ihe  horse- 
power, velocity  and  square  section  of  belts  ;  (3)  The  thickness  and  width  of  belts  ;  (4)  The 
square  section  of  belts  at  different  strains  per  square  inch.  For  office  use,  printed  on 
cardboard,  with  metal  edges  and  suspender,  price  2s. ;  post  free,  2S.  2d.  For  the  pocket, 
mounted  on  linen,  in  strong  case,  2s  6d. ;  post  tree,  2s.  8d. 

May— MAY'S  POPULAR  INSTRUCTOR  EOR  THE  MANAGE- 
MENT OF  ELECTRIC  LIGHTING  PLANT.  An  indispensable  Handbook  for  persons 
in  charge  of  Electric  Lighting  Plants,  more  particularly  those  with  slight  technical 
training.  Pocket  size,  price  2s.  6d. ;  post  free,  2s.  8d. 

May— MAY'S  TABLE  OF  ELECTRIC  CONDUCTORS.     Showing 

the  relations  between:— (i)  the  sectional  area,  diameter  of  conductors,  loss  of  potential, 
strength  of  current,  and  length  of  conductors  ;  (2)  the  economies  of  incandescent  lamps, 
their  candle-power,  potential,  and  strength  ot  current  ;  (3)  the  sectional  area,  diameter 
of  conductors,  and  strength  of  current  per  square  inch.  For  office  u  e,  printed  on  card- 
board, with  metal  edges  and  suspender.  Price  2s. ;  post  free,  2s.  2d,  For  the  pocket, 
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Phillips— THE    BIBLIOGRAPHY    OF    X-RAY    LITERATURE 

AND  RESEARCH.  Being  a  carefully  and  accurately  compiled  Ready  Reference  Index 
to  the  Literature  on  Rontgen  or  X-Rays.  Edited  by  Charles  E.  S.  Phillips.  With  an 
Historical  Retrospect  and  a  Chapter,  "  Practical  Hints,"  on  X-Ray  work  by  the  Editor. 
Price  55.  post  free. 

Pritchard— THE    MANUFACTURE    OF    ELECTRIC    LIGHT 

CARBONS.     By  O.  G.  Pritchard.     A  Practical  Guide  to  the  Establishment  of  a  Carbon 

Manufactory.     Fully  illustrated.     Price  is.  6d.,  post  tree  is.  qd. 

The  object  of  Mr.  Pritchard  in  preparing  this  work  for  pub  ication  was  to  enable  Pritish 
manufactuiers  to  compete  with  those  of  France,  Austria,  Germany  and  Bohemia  in  th«-  pro- 
duction of  electric  arc  carbon  candles.  The  book  is  fully  illustrated  and  gives  technical  d  tails 
for  the  establishment  and  working  of  a  complete  carbon  factory. 

Ram— THE   INCANDESCENT   LAMP   AND   ITS    MANUFAC- 
TURE.    By  Gilbert  S.  Ram.     Fully  Illustrated.     Price  is.  6d.  post  free. 
The  Author  has  endeavoured  to  give  such  information  as  he  has  acquired  in  the  course  of  a 
considerable  experience  in  Lamp-making,  and  to  present  that  information  with  as  little  mathe- 
matical embellishment  as  possible.    The  subjects  dealt  with  include  : — The  Filament :  Preparation 
ot  the  Filament,  Carbonising,  Mounting,  Flashing,  Sizes  of  Filaments,  Measuring  the  Filaments; 
Glass  Making  and  Blowing,  Sealing-in,  Exhausting,  Testing,  Capping,  Efficiency  and  Duration, 
and  Relation  between  Light  and  Power. 

Raphael— THE  LOCALISATION  OF  FAULTS  IN  ELECTRIC 

LIGHT  MAINS.     By  F.  Charles  Raphael.     New  Edition.     Price  7s.  6d.  nett. 

Although  the  localisation  of  faults  in  telegraph  cables  has  been  dealt  with  fully  in  several 
hand-books  and  pocket-books,  the  treatment  of  faulty  electric  light  and  power  cables  has  never 
bren  discussed  in  an  equally  comprehensive  manner.  The  conditions  of  the  problems  are, 
however,  very  different  in  the  two  cases ;  faults  in  telegraph  cables  are  seldom  localised  before 
their  resistance  has  become  low  compared  with  the  resistance  ot  the  cable  itself,  while  in  electric 
light  work  the  contrary  almost  always  obtains.  This  fact  alone  entirely  changes  the  method  of 
treatment  required  in  the  latter  case,  and  it  has  been  the  Author's  endeavour,  by  dealing  with  the 
matter  systematically,  and  as  a  separate  subject,  to  adequately  fill  a  gap  which  has  hitherto 
existed  in  technical  literature. 

The  various  methods  of  insulation  testing  during  working  have  been  collected  and  discussed, 
s.s  these  tests  may  be  considered  to  belong  to  the  subject. 

"THE  ELECTRICIAN"  PRINTING  &  PUBLISHING  CO.,  LTD., 
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(     9     ) 
Raphael— "THE  ELECTRICIAN"  WIREMAN'S,  LINESMAN'S 

AND  MAINS  SUPERINTENDENT'S  POCKET-BOOK.  A  Manual  for  the  Mains 
Superintendent,  the  Wiring  Contractor  and  the  "Wireman.  Edited  by  F.  Charles 
Raphael.  New  Edition.  Price  55.  nett,  post  free  55.  3d. 

EDITOR'S  NOTE. — When  the  preparation  of  this  Pocket-Book  was  commenced,  the  original 
intention  of  its  Editor  was  to  collect  in  a  handy  and  useful  foim  such  Tables,  Instructions 
and  Memoranda  as  would  be  useful  to  the  Electric  Light  Wireman  in  his  work.  This  has 
been  carried  out  in  Section  A  of  the  Pocket-Book.  During  the  past  few  years,  however, 
many  inquiries  have  been  received  for  a  good  book  dealing  with  the  laying  of  underground 
mains,  and  with  matters  connected  with  insulated  conductors  generally.  It  was  decided,  there- 
fore, to  extend  greatly  the  area  covered  by  the  book,  and  to  treat  the  whole  subject  of  erecting 
and  laying  electrical  and  conducting  systems  in  such  a  manner  that  the  tables,  diagrams  and 
letterpress  might  be  useful  to  engineers  in  charge  of  such  work,  as  well  as  to  the  wireman, 
jointer,  and  foreman.  In  fact,  the  section  on  Underground  Work  has  been  compiled  largely 
with  a  view  to  meeting  the  requirements  of  Mains  Superintendents,  Central  Station  Engineers, 
and  those  occupied  in  designing  networks. 

In  addition  to  the  tables,  instructions  and  other  detailed  information  as  to  cables,  ducts, 
junction  boxes,  &c.,  contained  in  the  section  on  Underground  Mains.it  has  been  deemed  advisable 
to  add  a  chapter  briefly  describing  the  various  systems  employed  for  public  distributing  networks. 
In  this,  essential  practical  information  is  alone  given;  two  and  three-phase  systems  are  dealt 
with,  as  well  as  continuous  current  and  single  phase,  and  the  method  of  calculating  the  size  of 
the  conductors  and  the  fall  of  pressure  from  the  number  of  lamps  or  horse-power  of  motors  is 
made  clear  without  the  elaboration  of  clock-face  diagrams  or  algebraical  exercises. 

Diagrams  for  the  connections  of  telephones  are  given  in  Section  D,  including  those  for 
subscribers'  instruments  on  the  British  Post  Office  exchange  system  in  London. 

Sayers— BRAKES  FOR  TRAMWAY  CARS.    By  Henry  M.  Sayers, 

M.I.E.E.    Illustrated.     35. 6d.  nett.     Now  Ready. 

Snell— ELECTRIC     MOTIVE    POWER.      By  Albion    T.   Snell. 

Over  400  pages,  nearly  250  illustrations.  Price  IDS.  6d.  post  free;  abroad,  us. 
The  rapid  spread  of  electrical  work  in  collieries,  mines  and  elsewhere  has  created^  demand 
for  a  practical  book  on  the  subject  of  transmission  of  power.  Though  much  had  been  written, 
there  was  no  single  work  dealing  with  the  question  in  a  sufficiently  comprehensive  and  yet  practical 
manner  to  be  of  real  use  to  the  mechanical  or  raining  engineer;  either  the  treatment  was  adapted 
for  specialists,  or  it  was  fragmentary,  and  power  work  was  regarded  as  subservient  toithe  question 
of  lighting.  In  general,  the  Author's  aim  has  been  to  give  a  sound  digest  of  the  theory  and 
practice  of  the  electrical  transmission  of  power,  which  will  be  of  use  to  the  practical  engineer. 

Shaw— A  FIRST- YEAR  COURSE  Oe'  PRACTICAL  MAGNET- 

ISM  AND  ELECTRICITY.  By  P.  E.  Shaw,  B.A.,  D.Sc.,  Senior  Lecturer  and  Demon- 
strator in  Physics  at  University  College,  Nottingham.  Price  2s.  6d.  nett ;  2s.  gd.  post  free. 
The  many  small  books  on  Elementary  Practical  Physics,  which  are  suitable  for  schools  or 
for  university  intermediate  students,  all  assume  in  the  student  a  knowledge  of  at  least  the  rudi- 
ments of  algebra,  geometry,  trigonometry  and  mechanics.  There  is,  however,  a  large  and  grow- 
ing class  of  technical  students  who  have  not  even  this  primitive  mathematical  training,  and  who 
cannot,  or  will  not,  acquire  it  as  a  foundation  for  physical  science.  Their  training  as  boys  in  a 
primary  school  has  not  been  supplemented  or  maintained  until,  as  skilled  or  unskilled  artisans, 
they  find  they  require  some  knowledge  of  electricity  in  their  daily  work.  They  enter  the  labora- 
tory and  ask  for  an  introduction  to  such  fundamentals  of  the  subject  as  most  affect  the  arts  and 
crafts.  On  the  one  hand,  mere  qualitative  experiments  are  of  little  use  to  these  (or  any  other) 
students;  on  the  other  hand,  mathematical  expressions  are  stumbling  blocks  to  them.  In 
attempting  to  avoid  both  these  evils.  I  have  sought  to  make  the  experimental  work  as  quantitative 
as  possible,  yet  to  avoid  mathematics.  As  novelties  in  such  a  work  as  this  the  ammeter  and  volt- 
meter are  freely  introduced,  also  some  simple  applications  of  the  subject— e.g.,  the  telephone, 
telegraph,  &c.  There  are  three  introductory  exercises,  six  exercises  on  magnetism,  twenty  on 
electricity  and  six  on  the  applications.  Nothing  is  done  on  statical  electricity  or  alternating 
currents,  for  the  reason  that  in  a  simple  course  like  this  they  are  considered  relatively  unimportant 
as  well  as  difficult. — Extract  f>om  Preface. 

Soddy— RADIO-ACTIVITY  :     An   Elementary   Treatise   from   the 

Standpoint  of  the  Disintegration  Theory.  By  Freak.  Soddy,  M.A.  Fully  Illustrated,  and 
with  a  full  Table  of  Contents  and  extended  Index.  6s.  6d.  nett. 

Extract  from  A  uthor1  s  Preface. — In  this  book  the  Author  has  attempted  to  give  a  con- 
nected account  of  the  remarkable  series  of  investigations  which  have  followed  M.  Becquerel'i 
discovery  in  1896  of  a  new  property  of  the  element  Uranium.  The  discovery  of  this  new  pro- 
perty of  self-radiance,  or  "radio-activity,"  has  proved  to  be  the  beginning  of  a  new  science,  in 
the  development  of  which  physics  and  chemistry  have  played  equal  parts,  but  which,  in  the 
course  of  only  eight  years,  has  achieved  an  independent  position.  .  .  .  Radio-activity  has 
passed  from  the  position  of  a  descriptive  to  that  of  a  philosophical  science,  and  in  its  main 
generalisations  must  exert  a  profound  influence  on  almost  every  other  branch  of  knowledge. 
It  has  been  recognised  that  there  is  a  vast  and  hitherto  almost  unsuspected  store  of  energy  bound 
m,  and  in  some  way  associated  with,  the  unit  of  elementary  matter  represented  by  the  atom  of 
Dalton.  .  .  .  Since  the  relations  between  energy  and  matter  constitute  the  ultimate  ground- 
work of  every  philosophical  science,  the  influence  of  these  generalisations  on  allied  branches  of 
knowledge  is  a  matter  of  extreme  interest  at  the  present  time.  It  would  seem  that  they  must 
effect  sooner  or  later  important  changes  in  astronomy  and  cosmology,  which  have  been  long 
awaited  by  the  biologist  and  geologist. 

The  object  of  the  book  has  been  to  give  to  Students  and  those  interested  in  all  departments 
of  science  a  connected  account  of  the  main  arguments  and  chief  expeiimental  data  by  which  the 
results  so  far  attained  have  been  achieved. 

"THE   ELECTRICIAN"  PRINTING  &  PUBLISHING  CO.,  LTD., 
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Telephony— BRITISH  POST  OFFICE  TELEPHONE  SERVICE. 

An  illustrated  description  of  the  Exchanges  of.  the  Post  Office  Trunk  and  Metropolitan 
Telephone  Services,  giving  much  interesting  information  concerning  these  Exchanges. 
Now  ready,  8vo,  very  fully  illustrated.  Price  2s.  6d.  nett. 

In  this  work  an  illustrated  description  is  given  of  the  Trunk,  Central  and  other  Exchanges 
ol  the  British  Post  Office  Telephone  Service  in  the  London  Metropolitan  area.  The  descriptions 
of  the  various  exchanges  are  complete,  and  the  illustratu  ns  show  the  disposition  ot  the  plant  and 
the  types  of  all  the  apparatus  used.  In  view  of  the  early  acquisition  by  the  Post  Office  of  the 
undertaking1  of  the  National  Telephone  Company  this  work  is  of  considerable  interest. 

MINUTES     OF     THE      PROCEEDINGS     AT     THE      HULL 

TELEPHONE  INQUIRY.     Price  3s.  nett,  post  free  3s.  6d. 

MINUTES  OF  THE  PROCEEDINGS  AT  THE  PORTSMOUTH 

TELEPHONE    INQUIRY.     Price  is.  6d.  nett,  post  free  is.  od. 

Thompson— THE  ELECTRIC  PRODUCTION  OF  NITRATES 

FROM  THE  VTMOSPHERE.    By  Prof.S.  P.  Thompson,  IXSc.,  F.K.S.  Ready  shortly. 

Wade— SECONDARY  BATTERIES  :  THEIR  MANUFACTURE 

AND  USE.    By  E.  J.  Wade.  Now  ready.   5oopages.    265  Illustrations.    Price  ios.6d.  nett. 

In  this  work  the  Author  deals  briefly  with  the  Theory  and  very  fully  with  the  Chemistry, 
Design,  Construction  and  Manufacture  of  Secondary  Batteries  or  Accumulators.  Prospectuses, 
post  free,  on  application. 

The  scope  of  Mr.  Wade's  important  work  covers  t>>e  whole  class  of  apparatus  embraced  in 
the  theory,  construction  and  use  ot  the  secondary  battery.  The  major  portion  of  the  book  treats 
the  accumulator  purely  from  the  point  of  view  of  an  appliance  which  fulfils  an  important  and 
definite  purpose  in  electrical  engineering  practice,  and  whose  manufacture,  use  and  properties 
must  be  understood  just  as  fully  as  those  of  a  generator  or  a  transformer.  The  <  oncluding 
chapter  (X.)  gives  a  complete  description  of  all  modern  electrical  accumulators.  Ihe  book 
contains  265  illustrations  and  a  very  copious  index. 

Weymouth— DRUM    ARMATURES    AND    COMMUTATORS 

(THEORY  AND  PRACTICE).  By  F.  M.  Weymouth.  Fully  Illustrated.  Price  ys.  6d. 
post  free. 

Wilkinson— SUBMARINE  CABLE-LAYING  AND  REPAIRING. 

By  H.  D.  Wilkinson,  M.I  E.E.,  &c.   Over  400  pages  and  200  specially  drawn  illustrations. 

Price  i2s.  6d.  post  free.     Ntw  Edition  in  prepaiation. 

This  work  describes  the  procedure  on  board  ship  when  removing  a  fault  or  break  in  a 
submerged  cable  and  the  mechanical  gear  used  in  different  vessels  for  this  purpose  ;  and  considers 
the  best  and  most  recent  practice  as  regards  the  electrical  tests  in  use  for  the  detection  and 
local isati on *of  faults,  and  the  various  difficulties  that  occur  to  the  beginner.  It  gives  a  detailed 
technical  summary  of  modern  practice  in  Manufacturing,  Laying,  Testing  and  Repairing  a  Sub- 
marine Telegraph  Cable.  The  testing  section  and  details  of  'boardship  practice  have  been  prepared 
•with  the  object  and  hope  of  helping  men  in  the  cable  services  who  are  looking  further  into  these 
branches. 

Young— ELECTRICAL   TESTING  FOR   TELEGRAPH   ENGI- 
NEERS.    By  J.  Elton  Young.      Very  fully  illustrated.     Price  IDS.  6d.,  post  free  us. 
This  book  embodies  up-to-date  theory  and  practice  in  all  that  concerns  everyday  work  ot 
the  Telegraph  Engineer. 

CONTENTS. 


Chapter    I.— Remarks  on  Testing  Apparatus, 

,,  II. — Measurements  of  Current,  Poten- 
tial, and  Battery  Resis- 
tance. 

„      III.— Natural  and  Fault  Current. 

,,  IV.— Measurement  of  Conductor  Re- 
sistance. 

,,  V. — Measurement  of  Insulation  Re- 
sistance. 

„  VI. — Corrections  for  Conduction  and 
Insulation  Tests. 


Chapter  VII. — Measurement  of  Inductive  Capa- 
city. 

,,  VIII.  — Localisation  of  Disconnections. 

„  IX.— Localisation  of  Earth  and  Con- 
tacts. 

,,        X. — Corrections  of  Localisation  Tests. 

,,  XL— Submaiine  Cable  Testing  during 
Manufacture,  Laying  and 
Working. 

,,  XII. — Submarine  Cable  Testing  during 
Localisation  and  Repairs. 


In  the  Appendices  numerous  tables  and  curves  of  interest  to  Telegraph  Engineers  are  given. 

THE  INTERNATIONAL  TELEGRAPH   CONVENTION  AND 

SERVICE  REGULATIONS.  (London  Revision,  1903).  The  complete  Official  Fr-ncn 
Text  with  English  Translation  in  parallel  columns,  by  C.  E.  J.  Twisaday  (India  Cffic'-, 
London),  Geo.  R.  Neilson  (Eastern  Telegraph  Co.,  London),  and  officially  revised  by 
permission  of  H.B.M.  Postmaster-General.  Cloth  (foolscap  folio),  6s.  nett ;  (demy  iolio), 
8s.  6d.  nett,  or  foolscap,  interleaved  ruled  paper,  8s.  6d.  nett. 

INTERNATIONAL     RADIO-TELEGRAPHIC     CONFERENCE, 

BERLIN,  October-November,  1006,  with  the  International  Radio-Telegraphic  Conven- 
tion, Additional  Undertaking,  Final  Protocol  and  Service  Regulations  in  French  and 
English.  Officially  accepted  Translation  into  English  of  the  complete  Proceedings  at 
this  Conference.  This  translation,  which  has  been  made  by  Mr.  G.  R.  Neilson,  is  pub- 
lished under  the  authority  of  H.  H.M.  Postmaster-General,  and  is  accepted  as  official  by 
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"THE  ELECTRICIAN"  PRIMERS 


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Edited  by  Mr.  W.  R.  COOPER,  M.A.,  R.Sc.,  M.I.E.E. 

There  are,  in  all,  over  FO  PRIMERS  in  this  Collection.  The  complete  set  comprises  over  1,000  Pages 
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umes, and  consequently  Copyright.  Following  is  a  list  of  the  subjects  dealt  with  :— 


THEORY    (25 

Primers.)  Price  3s.  6d.  nett. 
(For  price  of  Single  Copies 
see  below.) 

1.  Effects  of  an  Electric  Current 

2.  Conductors  and  Insulators 

3.  Ohm's  Law 

4.  Electrical  Units.. 

5.  Curves  and  their  Uses 

6.  Primary   Batteries 

7.  Arrangement  of  Batteries 
Electrolysis 

9.  Secondary  Batteries 

10.  Alternating  Currents 

11.  Lines  of  Force    . . 

12.  Magnetism  and  the  M 

Properties  of  Iro: 
18.  Galvanometers  . . 
U.  Electrical  Measuring  Instr 

ments 

16.  Electrical  Measurements 

16.  Electricity  Meters  Direct  Cu 

rent)       

16x.  Ditto   (Alternating  Curren 

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agnet 


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Technical  Words, 
Terms  and  Phrases, 
to  aid  the  Student,  Artisan  and 
General  Reader  in  his  compre- 
hension of  the  sub'ects  dealt 
with.  Each  individual  Primer 
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Books,  &c.,  to  be  consulted 
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ticular subject  is  desired  to  be 
extended. 


Vol.  II.     Price  6s.  nett.    (For  Price  of 
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ELECTRIC  TRACTION, 

ELECTRIC  LIGHTING  and 

ELECTRIC    POWER 

(31  Primers.) 


25  Dynamos  and  Direct  Current  Motors 
26.  Alternators  and  Alternate  -  Current 

Motors        

27  Transformers  and  Converters.. 

28.  Testing  Electrical  Machinery  . . 

29.  Management  of  Dynamos  and  Elec 

trie  Machinery 

30.  Electric  Wires  and  Cables 

31.  Underground  Mains 

32.  Switchboards  

33.  .switch hoard  Devices 

34.  Systems  of  Elec.  Distribution  .. 

35.  hlectric  Transmission  of  Power 

36.  Tramway  Traction  by  TROLLEY 

37.  Tramway  Traction  by  CONDUIT 

88.  Tramway  Traction  by  SURFACE  CON 

TACT 

39.  Tramway  Traction  by  ACCUMULA 

40.  Electric  Railways— Surburban  Lin 

41.  Electric  Automobiles 

42.  Electric  Ignition 

4t.  Incandescent  Lamps 

44.  Arc  Lamps 

45.  Street  J  tenting       

46.  House  Wiring  for  Electric  Light 

47.  Electric    Driving  iu    Factories   an 

Electric  Cranes. . 

48.  Electric  Lifts 

49.  Steam  Engines 

50.  Steam  Boilers          

1.  The  Equipment  of  Electricity  Gene 

rating  Stations , 

52.  Gas  and  Oil  Engines 

53.  Producer  Plant       

54.  Comparative   Advantages   of    Steam 

and     Producer     Gas    for     Power 
Production  

55.  Designing  and  Estimating  for  Small 

Installations 


(8) 

I 

fs 

(11) 

(23 

(11) 

si 


(18) 

H 

(2) 
(3) 
(8) 
(14) 

(7) 

(The  figures  in  parentheses  indicate  the  number  of  Illustrations.) 

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TELEGRAPHY, 
TELEPHONY, 
ELECTROLYSIS  and 
MISCELLANEOUS 
APPLICATIONS  OF 
ELECTRICITY. 

(25  Primers.) 

Telegraphy:— 

56.  Elements  of  Land,  Submarine   and 
Wireless 

58  Double-Current  Working 

59.  Diplex  and  Quadruplex 

60.  Multiplex        

61.  Automatic      Telegraph       Apparatus 

(Wheatstone    Transmitter,     iuto. 
Curb   Transmission,  Auto.  Trans- 
mission for  Submarine  Cables) 
62   Cable  Stations:  General  Working  and 
Electrical  Adjustments 

63.  Laying,  Jointing  and  Repair  of  Sub- 

marine Cables 

64.  Testing  Submarine  Cables 

65.  Testing  Land  Lines 

66.  Aerial  Telegraph  Line   Construction 

and  Jointing        

67.  Wireless  Telegraphy       

Telephony:— 

68.  The  Telephone        

69.  Telephone  Sets       

70.  Telephone  Exchanges 

71.  Telephone  Lines 

72.  Electric  Jiell   Fitting  and    Internal 

Telephone  Wiring        

Miscellaneous  :— 

73.  Electric  F eating  &  Cooking 

74.  Electric  Welding    ..        ..  '     .. 

75.  Electric  Furn'ces 

76.  Electro-Deposition 

77.  Industrial  Electrolysis 

78.  Photo  Engraving 

79.  Electric  (-locks       

80.  Block  Signalling  on  Hallways. . 


WIRELESS    TELEGRAPH     CONFERENCE,    BERLIN,    1903, 

Full  Report  of  the  Proceedings  at  the  Conf-rence.  Translated  into  English  by 
G.  R.  Neilson.  Officially  accepted  by  the  Post  Office  Authorities.  Bound  Cloth,  8s.  6d., 
post  free  8s.  qd.,  abroad  QS. 

Parshall  and  Hobart— ARMATURE  WINDINGS   OF   ELEC- 
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Part  I.,  Continuous-current  Armature  Windings;   Part   II.    Windings  for  Alternate-cur- 
rent Dynamos  and  Motors  ;  Part  III.,  Winding  Formula-  and  Tables. 

Woods— AETHER  :   A   Theory  of   the  Nature  of  /Ether  and  of  its 

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ELECTRICITY  IN  MINES.— Under   the  new  Rules  and    Regula- 

tions  concerning  the  Use  of  Electricity  in  Mining  Operations,  it  is  compulsory  that 
directions  for  the  effective  Treatment  of  Cases  of  Apparent  Death  from  Electric  Shock  be 
conspicuously  placed  in  certain  prescribed  positions  in  the  Mines. 

A  set  of  these  DIRECTIONS,  with  illustrations  showing  the  method  of  application, 
accompanied  by  PRECAUTIONS  to  be  adopted  to  prevent  danger  from  the  electric  current, 
and  INSTRUCTIONS  for  dealing  with  BROKEN  ELECTRIC  WIRES,  is  now  ready. 

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Abbott— TELEPHONY.      By   A.   Vaughan   Abbott.      In   six  vols. 

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Arnold  —  KONSTRUKTIONSTAFELN  FUR  DEN   DYNAMO- 

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